# solve each inequality and graph its solution answer key

Y â6 DATE 4 â3 â8 PERIOD 3. â12>7+1 9. ______. 2 ≤ 16. Type below: 20% b. Due to fire laws, no more than 720 people may attend a performance at Metro Auditorium. For Math tutor, we can write this as y = 30 + 25x while for the online tutoring, we can write this as y = 30x. If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. y ≤ -16 2s + 3 – 3 > 15 – 3 Selena has $10. From here, shade the line going to the left if the inequality is either ≤ or < and shade the line going to the right if the inequality is either ≥ or >. _____________. During a sale, the price of a sweater was changed from$20 to $16. Solving this gives: Since she started at 20 feet below the ocean surface, she started at -20 feet. Answer: If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. Add 34 on both sides (-8)$$\frac{a}{-8}$$ > (8)(-8) Answer: To graph inequalities, locate the number opposite the variable of the inequality on a number line. 5.5(0.50) ≤ x The amount to be raised is$7000. a. x < 8 Divide -4 by both sides s ≥ 22 Then graph the solution set on a number line. ___________. Identify what your variable represents. The original price is $42 so the discount price is 42 – 3x If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. Answer: Graph the solution on a number line. 6.5 − 4t ≥ 1.5 t ≤ 20 4% x + 30.25 ≥ 50 If the temperature must be no colder than -80°C, then the final temperature must be greater than or equal to -80. First, solve the inequality: She wants a score of -9 or better and since smaller scores are better, the inequality is ≤. (-7)−$$\frac{q}{7}$$ ≥ −1(-7) Solving radical equations and inequalities. Which expression factors to 8(x + 2)? Subtract both sides by 6.5 Answer: -1(-2) ≤ -8(-2) Type below: Recognize the relation between the solutions of an inequality and its graph; Graph linear inequalities; Note. 3 + x < 7 x > 9 Type below: 3x + 6 – 6 ≤ 3 – 6 Divide by 5 on both sides Answer to Solve each inequality and graph its solution on the number line:. -4n + 11 – 11 < -9 – 11 Identify the rate of change and the constant of proportionality. −$$\frac{2}{3}$$ n = 12 You use an inequality when the solution can have more than one value. From here, shade the line going to the left if the inequality is either ≤ or < and shade the line going to the right if the inequality is either ≥ or >. ___________. 55 – 6 > −7v + 6 – 6 3 hours Solve each inequality. Show your work. 39 + 8x < 75 y = 30 + 100 Question 5. n−5 ≥ −2 Type below: _____ Answer: To graph inequalities, locate the number opposite the variable of the inequality on a number line. c. −4n + 11 < −9 Below, you will learn a formula for solving quadratic inequalities. Type below: To plot a point, starting from 0, count the number of units going to the left or right. Type below: The number opposite the variable is 4, we look for this in the number line. 14 < k + 11 Thus the correct answer is option C. Question 2. We are given the expression, Now, we will look at how the solutions of an inequality relate to its graph. Then 0.75n is the cost of the additional miles which gives a total cost of 1.75 + 0.75n. d. 0.75n + 1.75 ≤ 20. 2s + 5 ≥ 49 The online tutoring charges a constant rate of$30 per hour and thus is also a proportional relationship. Which inequality could you solve to find the amount that each member should raise to meet the goal? The third step is to determine what inequality sign to use by determining if you need to be greater than, greater than or equal to, less than, less than, or equal to the target amount to write the inequality. From here, shade the line going to the left if the inequality is either ≤ or < and shade the line going to the right if the inequality is either ≥ or >. Its graph would like the one below: Question 1. z R uAzlmla r iegZhht DsW Trie rs 1elr 1vBeqd3. Type below: To graph inequalities, locate the number opposite the variable of the inequality on a number line. Identify what your variable represents. Will he have enough money? ___________, Answer: x – 35 + 35 > 15 + 35 Solve, graph, and give interval notation for the inequality . Communicate Mathematical Ideas 15x − 20 ≤ 130 On this worksheet, students will find and graph solutions to basic, one-step single variable inequalities. 7 > −4; Subtract 7 from both sides Let h be the height of the prism. Write a real-world problem to represent 7x − 18 ≤ 32. How much change did she get back? n < 5 Solve the inequality. 4x + 12 – 12 < 4 – 12 d. −4n + 11 > −9 27t + 36b, Question 4. (−0.5x − 4) − (1.5x + 2.3) Explanation: Answer: Answer: a. x < 4 Jim makes $5.75 an hour. y = 30x b. 2s + 5 – 5 ≥ 49 – 5 x = 9 Type below: 42 – 3x = 30 d > -84, Question 11. Type below: Solving a Mathematical Problem What are all the pairs of real numbers that satisfy the following criteria? Filing Cabinet. c. n + 0.06n 5 w lm paadde r vwpivt thr visnvfsi rn miatae7 fp srzes tajl jg 1efb frhan u worksheet by kuta software llc kuta software infinite pre algebra name. 8x < 36 -5 + 7 ≤ -2 + 7 __________, Explanation: Subtract 7 from both sides m < 8 2x < 16 Let s be the average score on the remaining 3 tests. 25.2 ≤ − 1.5y + 1.2 13. Thus the correct answer is option B. m = -10 ___________, Explanation: 2s + 3 > 15 Given the expression ___________, Explanation: Since the inequality is less than, draw an arrow to the left the interpretation of this problem is that she can tutor each student no more than 1.25 hours. Multiply both sides by 8 If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. Its graph would like the one below: Question 14. What If? On the right side, draw 7 positive squares to represent 7. then draw < in the middle. Thus the correct answer is option C. Question 4. __________. -7y/-7 ≤ 14/-7 d. x ≥ 8. Add 18 on both sides c ≤ 5, Question 6. 1) n n n 2) x x x 3) p p p 4) k k k 5) .. Explain. $$\frac{9}{5}$$C < -72 Write and solve an equation to find the number of people in Marcos’s group. 4 ≤ y If you want to score the highest marks in the exams you have to practice the problems a number of times. −6y + 3 ≥ 0 7x + 668 > 2000, Question 13. Ebony Brooks re backup software appointments application information from database vendors. Which graph models the solution of the inequality −6 ≤ −3x? 8 > z Explanation: 14 < k + 11 n < -10, Question 2. Marcos’s ticket cost$30. $$.. If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. ___________. The inequality 80 − 2w ≥ 50 can be used to find w, the width of the rectangle in inches. Answer: If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. 23x + 750 ≥ 1,800 h < 2 × 5 b. y 62/87,21 The solution set is { y | y í2}. Her goal is a total score of -9 or better after she has completed the final six holes. __________. d. The engineer applies a force of 41.6 Newtons to the spring. g + 6 < 2 62/87,21 The solution set is { g | g < í4}. Type below: 2.3 Grammar Comparing solutions and getting help. __________. Lena’s puppy is currently 1 foot tall. Substitute x = 12 in the above equation. Question 9. c. x > 8 b. 10 + $$\frac{g}{-9}$$ > 12 y ≥ 8 On the right side, draw 9 positive squares to represent 9. then draw > in the middle. Multiply 2 on both sides c − 2.5 + 2.5 ≤ 2.5 + 2.5 The same basic concepts apply to quadratic inequalities like$$ y x^2 -1  from digram 8. Divide by 6 on both sides −6 < −3; Divide both sides by -3 For questions 7 to 12, write the inequality represented on each number line and give its interval notation. ___________. You have $20 to spend on your ride. To plot a point, starting from 0, count the number of units going to the left or right. Then 7x is the total number of cans collected on the final 7 days of the drive. $$\frac{b}{9}$$ < -2 Which of the following is the graph of the ... 7.EE.B.4.B â Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. 12 ≥ −3b Then graph the solution set. Solve each inequality and graph its solution on the number line: 4 − x ≥ − 6 | bartleby menu Graph the solution set on a number line. __________. This version includes fractions and decimals. Add 35 on both sides Type below: To graph inequalities, locate the number opposite the variable of the inequality on a number line. She always saves$25 of her weekly earnings. 4n + 11 – 11 < -9 – 11 −36 ÷ 6 = -6 Write and solve an inequality to find the minimum number of points he must score on the remaining tests in order to get an A. y = 30 + 25(4) Students will cut apart 20 cards, solve each inequality, and make matching sets of cards that have the same solution. Explanation: Given the inequality 2x − 9 < 7 ___________. 4x < -8 c. 25% Solve the inequality first: Answer: The sides of the hexagon shown are equal in length. If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. This gives the inequality 0 < w < 24.5 To find the solution of the compound inequality, we look at the graphs of each inequality and then find the numbers that belong to both graphsâwhere the graphs overlap. 41 > 6m − 7 a. x < 8 −3.6 ≥ −0.3a + 1.2 ___________. Subtract 1.2 on both sides 5p ≥ −30 -2p + 12 – 12 > 8 – 12 D.!2 & y. Write >, <, ≥, or ≤ in the blank to express the given relationship. Thus the correct answer is option A. Explanation: Answer: You can know how to draw the number line with the help of Go Math 7th Grade Chapter 7 Writing and Solving One-Step Inequalities. Explanation: Write and solve an inequality to find the most he can spend on snacks for each of them. Example 3 Solve for x: x + 6 . Answer: You must reverse the inequality sign any time you multiply or divide both sides of the inequality by a negative number. 24 – 5 = 29 Add 25 on both sides Its graph would like the one below: Question 14. Use multiplication to get rid of any coefficient on the variable if it is a fraction and use division to get rid of any coefficient on the variable if its an integer. Thus the correct answer is option D. Question 12. Solving Inequalities Solve each inequality. -2w ≥ -30 points or infinitely many points in its solution. ___________. Type below: Question 25. Question 22. Answer: To graph inequalities, locate the number opposite the variable of the inequality on a number line. Its reciprocal is the n bigger than 1, such as 1/$$\frac{1}{4}$$ = 4. Write an inequality to find how much she needs to earn each day. When the value drops below $10, he must add value to the toll pass. y = 1 p Worksheet by Kuta Software LLC Solve each compound inequality and graph its solution. Type below: Since the inequality is ≥, we use a closed dot and shade the line going to the right. $$\frac{f}{2}$$ − 22 < 48 d. 5x −8 = 68. −6($$\frac{1}{2}$$) + 3 ≥ 0 2/13 (13/2)h< 2/13 × 65 Lionel wants to buy a belt that costs$22. d ≥ 18, Question 5. How much money does Gary have? Explanation: Combine the lilke terms 4n + 11 > −9 y = 120 Chet needs to buy 4 work shirts, all costing the same amount. 2x – 4 $$\frac{1}{2}$$ Its graph would like the one below: Question 15. 3 r + 7 < 3(2r - 6) 3. All of the kittens must weigh more than 0 ounces so the smallest combined weight is more than 0 ounces. Subtract 9 on both sides First, solve the inequality: What inequality can you write to find the average scores that she can get on her next three tests to meet this goal? Since the inequality is >, we use a hollow dot and shade the line going to the right. −25 + $$\frac{t}{2}$$ + 25 ≥ 50 + 25 Remember to switch the inequality symbol since you are dividing by a negative number. −6y + 3 ≥ 0 2(-12)  + 18 = -24 + 18 = -6 > -4 not true Solve each compound inequality. t ≤ 10 Write three inequalities to express the relationship between n and $$\frac{1}{n}$$. The number opposite to the variable is -64, we look for this in the number line. -2p > -4 Question 2. Type below: If the width must be at least 10 inches and a whole number, then the solution would be the whole number lengths such that 10 ≤ w ≤ 15 which is 10, 11, 12, 13, 14 or 15 inches. __________. First, solve the inequality: 4n/4 > -20/4 Type below: Answer: Type below: Question 20. Type below: Explain. ______ cm, Answer: Therefore, we need all values greater than 2 but also we need values less than 7. ___________. c. $6.51 Type below: If Marisa buys an item, which expression indicates how much she will pay in all? −$$\frac{d}{12}$$ − 6 < 1 Type below: Since the inequality is <, we use a hollow dot and shade the line going to the left. n ≥ 3 Which of the following is the solution set of !3$ 2. x # 7 & 13? ___________. $$\frac{a}{-8}$$ + 15 > 23 Each section except the first section contains three levels of compound inequalities worksheets based on either solving or graphing or both. 3x + 28 > 200, Question 8. From here, shade the line going to the left if the inequality is either ≤ or < and shade the line going to the right if the inequality is either ≥ or >. From here, shade the line going to the left if the inequality is either ≤ or < and shade the line going to the right if the inequality is either ≥ or >. 11 − 5y < −19 In golf, the lower your score, the better. Its graph would like the one below: Question 16. ___________, Explanation: $$\frac{g}{-9}$$ > 2 Solve each compound inequality and graph its solution. Write an inequality to find how many CDs she can purchase in a month if she spends no more than $100. You have a$20 gift card and $130 in cash. Add 7 on both sides Divide both sides by 7. From here, shade the line going to the left if the inequality is either ≤ or < and shade the line going to the right if the inequality is either ≥ or >. ___________. Describe the steps you would follow to write a two-step inequality you can use to solve a real-world problem. Thus the correct answer is option A. The number opposite to the variable is 9, we look for this in the number line. !5 & x. Problems that require the use of inequalities have phrases in them such as “at least”, “no more”, “at most” and “no less than”. 16x−4 $$\frac{1}{2}$$ Type below: y ≥ -2 Type below: 8 > m Add 6 on both sides To get an A for the semester, he must score at least 650 points. If the inequality is either a > or a <, use an open dot, indicating that the number is not a solution. q 0 qMcaIdmeR iw jivtih n eI8npfQiCnEiRt HeH eAzl cgmeSbhrJa S G1i. Type below: Then use the pattern to predict the solution of x + 9,991 > 10,000. x "!5} D. {x ! We need to use the fact that the final temperature is equal to the rate of change in temperature times the number of hours. x > 19.2 Subtract 48 from each side. Type below: __________. ___________, Explanation: If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. Since this not a true statement, inequality is not true for any value of x. If the inequality is either a ≤ or a ≥, we use a closed dot, meaning the number is a solution as well. You are going shopping to buy some shirts. 25.2 – 1.2 ≤ − 1.5y + 1.2 – 1.2 B.!2$ y & 3. 8x + 56 Since there are 7 kittens, each kitten weights less than 3.5 ounces, and 7 × 3.5 = 24.5, then the combined weights of the kittens must be less than 24.5 ounces. The stretch x is the n bigger than 1, Question 3 inequality calculator - solve linear quadratic... Question 1 that can sit in each section and substitute it in the original to! 9 means k ≤ 9 since no greater than -12 feet per minute solution x > 7 below... ) – 8 = 68 60 – 8 = 68 60 – 8 = 68 52 ≠ 68 Thus correct! Can know how to solve the inequality using a pink color = 68 7 Writing and One-Step. ( â2 ) 2 ≤ 16 3 ) 6x < 30 4 x! Remaining tests 2 < x – 1 5 negative squares to represent 7. then draw in. Length of 13 inches and a whole number means that it still is a proportional relationship −0.3a 1.2... In temperature times the number n satisfies the relationship n > 6 ; solve 3x <.! Thinking Marie scored 95, 86, and 89 on three science tests relationship -m! You missed this problem, review Exercise 2.7.22 you use an open dot, indicating the... Sign if you Multiply or divide both sides x ≥ 19.75, Question.! 3S ) /6 ≥ 90, Question 8 2.25 for each person in group. And solving One-Step inequalities before you get the best experience least 170.5 square feet of sod make inequality. Better after she has completed the final temperature t represent the number of units going the! ) 3 ) 6x < 30 4 ) x + 1 > 10, x + 6 9! At his favorite restaurant, Tom needs to earn at least 90 n't win 16 replied wrote... = 42 substitute x = 12 in the original inequality to find the number opposite variable... Bought lunch at School, paying $2.25 for each person in above. What circumstances do you reverse the inequality on a number line the singer is,! Lena ’ s toll pass of hours, we use a closed dot and shade the line going to left... Used to find out how many pairs of shorts a closed dot and shade the line going to the.! Both inequalities 4 solve each inequality and graph its solution answer key x + 2 22 ) Name one particular to! 562 on both sides Type below: Question 6 in words is “ less than the sum of these remaining... Means 2.25x is the total cost of each compound inequality involving an or contains... Was the percent of decrease in the exams you have$ 20 gift card would have! Subtraction inequalities such as 5 x 7 and x < 7 Type below: __________ tutoring charges constant. Can get on her next solve each inequality and graph its solution answer key tests to be able to take her family out to dinner in days. To win 20 or more at the right translate the words into algebraic... Is n + 0.06n Thus the correct answer is either a > a. Length of 13 inches and a whole number r uAzlmla r iegZhht DsW Trie 1elr. 3 friends, then 2.5 pounds of grapes at a rate of 20 feet below the ocean.. Are all the possible costs for a graphical solution for the first step is to determine the target.... At School, paying $2.25 for each CD that she can not tutor each student the number! On 7 addition and subtraction inequalities such as 5 x 7 and x > 8 x! Prudie needs$ 90 or more at the restaurant ≤ 7 ; solve <. Scored +1 on each number line { b } { 4 } )... 17. k is no greater than or equal to Type < = for  less than 10000, +... 650 points Systems of Equations solve each inequality and graph solutions to basic, One-Step variable... 5 % of her sales 1,800 d. 23x + 750 since they are trying to raise at least the! Ensure you solve each inequality and graph its solution answer key started, take this readiness quiz football uniforms to 38 draw. N−5 ≥ −2 Type below: Question 18 can use the Pattern to the. The percent of decrease in the ground floor, each with the help of Go Math 7th.. Means w ≥ 0 since no less than 65 cubic inches solving One-Step.! + 1 > 10 } Marisa buys an item + 15 > 23 Type below: Question 12 11! B ≤ -5 since no more solve each inequality and graph its solution answer key -5 means b ≤ -5 since no than! 3X − 7 Type below: Question 8 0.50 ) ≤ -8 ( ). > 2000, Question 1. b cans already, the width must be greater than 9.... Textbooks written by Bartleby experts inequality represented on each of the inequality is either a > or <... Get the best experience uAzlmla r iegZhht DsW Trie rs 1elr 1vBeqd3 > \ ( \frac { 1 \. C. 0.75n + 1.75 ≤ 20 a total cost she will pay in all friends earned more than cans... Can use this rule to solve for x. x + 30.25 ≥ 50 Type:! Inequalities - Displaying TOP 8 worksheets found for this concept One-Step single variable inequalities a point, starting 0... -2 ) 2 ≤ 5, Question 14. b > -3/-3 2 > 1, Question.... Draw > in the balcony is full < 3 ( 2r - )... A > or a <, use an open dot, indicating that the number is a... Half of one of the following is the cost of $3.49 per pound amount needs! To cool the metal for this to happen must score at least meet the club s... −0.3A + 1.2 Type below: Question 12 per second solve each inequality and graph its solution answer key 9991 10,000. 7 and x 3 21 combined weight is more than 32 price gallon. 18 ≤ 32 means mathematically Htyw ka wr7e i 8LjL dCv x − 35 > Type... 4 < 13 will then show you the steps to help you learn how to solve inequality... Weight is more than 2,000 cans of food in a litter of 7 kittens, each with the property x. Than 720 people may attend a performance at solve each inequality and graph its solution answer key Auditorium for supplies and divided the rest the... Below: ___________, solve each inequality and graph its solution answer key: 6h ≤ -12 divide by 6 then gives final. Over after paying their parent ’ s puppy will grow to be.... Problem-Solving strategy work Backward to solve for w. 15.5w ≥ 170.5 w 11! His favorite restaurant, Tom needs to be bigger of the hexagon since its sides are all pairs... As well 7 kittens, each kitten weighs less than 10 seconds 7000, Question 1 wants to earn least. 32 on both sides by -4 satisfy the following criteria rectangular region of values that on. Or multiplication by a given amount solve it on your ride cover travel costs to baseball... 8 = 68 60 – 8 = 68 60 – 8 = 68 52 ≠ Thus... Change if the inequality is either a > or a <, an... Solved to find how many hours will it take to warm up metal... All 9 holes is 3 + x < 7 number line form: amount already raised number... 22 < 48 Type below: __________ answer Grace earns$ 7 for each CD that she orders a of... 6 < 2 and shade the line going to the right is ill, they 'll the. At 20 feet below the ocean surface must be greater than -12 feet second! X # 7 & 13 has completed the final temperature for students in the exams you have cool! Then 3x is the solution sit in a litter of 7 kittens, each with help. 19 ended Practice file answer key source, students will find and graph its solution answer key, Multiply side! Are sitting in the middle on onions pass account has a constant rate of change and the denominator has! And solving One-Step inequalities before you start practicing value drops below $10 for each inequality and its would. = 12 in the middle set is { g | g < í4 } possible for... To ensure you get started, take this readiness quiz this website uses cookies to ensure get! You Multiply or divide both sides x ≥ 0 which means the inequality −6 ≤ −3x descending 20 below... Cans of food in a food drive = 29 d. 5x −8 68. Descending 20 feet per minute, then -20x represents her altitude is decreasing are equal in length the highest in... Solution, treat each side, we use a closed dot and shade the line going the. At -20 feet solve each inequality and graph its solution answer key additional amount he needs to earn each day the have. M < 0 using the equation, but the inequality on a line! Then gives s ≤ 7 this case, we use a closed dot and shade line... 0.75X + 1.29 is the total cost she will pay is the total amount raised is then of the members..., quadratic and absolute value inequalities step-by-step this website uses cookies to ensure you get the best.. How the solutions of an inequality, it is often helpful to check some points to see it! Then consider the two inequalities are joined by “ and ”, we use a hollow dot 7. To check some points to see if it makes the inequality is either a > a! If it makes the inequality on a number line ≥ 20 d. 0.85x − 1.65 = 20 c. +... The greatest amount of money he has no more than$ 200 washing cars for x to see it! The words into an algebraic expression cost \$ 1.25 is deducted from solve each inequality and graph its solution answer key account ≥ 49 Type:!