## Solving Linear Inequalities Chapter Review

**2.1 Writing and Graphing Inequalities **a. A number x plus 36 is no more than 40. Write this sentence as an inequality.b. Graph w > 3.

**Write the sentence as an inequality.**

Question 1.A number d minus 2 is less than -1.Answer:The given worded form is:A number d minus 2 is less than -1Hence,The representation of the given worded form in the form of inequality is:d 2 < -1

Ten is at least the product of a number h and 5.Answer:The given worded form is:Ten is at least the product of a number h and 5Hence,The representation of the given worded form in the form of inequality is:10 h

We can conclude that there is no solution to the given inequality

**2.5 Solving Compound Inequalities**

**Solve 1 2d + 7 9. Graph the solution.**

Question 21.A number x is more than -6 and at most 8. Write this sentence as an inequality. Graph the inequality.Answer:The given worded form is:A number x is more than -6 and at most 8The representation of the given worded form in the form of inequality is:x > -6 and x 8Hence,The representation of the solutions of the given worded form in the form of compound inequality is:-6 < x 8The representation of the compound inequality in the graph is:

**Solve the inequality. Graph the solution.**

Question 22.We can conclude that the compound inequality solution to the given inequality is:-2 z 6The representation of the compound inequality in the graph is:

**2.6 Solving Absolute Value Inequalities**

**Solve the inequality. Graph the solution, if possible.**

Question 24.

## Lesson 26 Solving Absolute Value Inequalities

**Essential QuestionHow can you solve an absolute value inequality? Solving an Absolute Value Inequality AlgebraicallyEXPLORATION 1Solving an Absolute Value Inequality AlgebraicallyWork with a partner.**Consider the absolute value inequality | x + 2 | 3.a. Describe the values of x + 2 that make the inequality true. Use your description to write two linear inequalities that represent the solutions of the absolute value inequality.b. Use the linear inequalities you wrote in part to find the solutions of the absolute value inequality.c. How can you use linear inequalities to solve an absolute value inequality?Answer:The given absolute value equation is:| x + 2 | 3

The following are the steps to solve the absolute value inequality:A) Isolate the absolute value expression on the left side of the inequalityB) If the number on the other side of the inequality sign is negative, then your equation either has no solution or all real numbers as solutionsC) Remove the absolute value bars by setting up a compound inequalityD) Solve the inequalities

c. How can you use a number line to solve an absolute value inequality?Answer:You begin the marking of the points on the number line by making it into separate equations and then solving them separately. An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative. You can write an absolute value inequality as a compound value inequality

**2.6 Lesson**

## Lesson 22 Solving Inequalities Using Addition Or Subtraction

**Essential Question**How can you use addition or subtraction to solve an inequality?**EXPLORATION 1****Quarterback Passing Efficiency****Work with a partner.**The National Collegiate Athletic Association uses the following formula to rank the passing efficiencies P of quarterbacks.Answer:The formula used to rank the passing efficiencies P of the quarterbacks is:By comparing the coefficients, we getY = 8.4

We can conclude that the value of p is greater than -3The representation of the inequality in the number line is:

**Monitoring Progress**

Question 7.The microwave oven uses only 1000 watts of electricity. Does this allow you to have both the microwave oven and the toaster plugged into the circuit at the same time? Explain your reasoning.Answer:Yes, this allows you to have both the microwave oven and the toaster plugged into the circuit at the same time

Explanation:It is given that the microwave oven uses only 1000 watts of electricity.We know that,The toaster consumes less electricity than the microwave ovenHence, from the above,We can conclude that 1000 watts of electricity allow you to have both the microwave oven and the toaster plugged into the circuit at the same time

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## Big Ideas Math Book Algebra 1 Answer Key Chapter 2 Solving Linear Inequalities

Practicing using the Big Ideas Math Algebra 1 Answer Key Ch 2 Solving Linear Inequalities and learn how to solve various questions easily. BIM Book Algebra 1 Chapter 2 Solving Linear Inequalities Solution Key will aid in your preparation and enhances your conceptual knowledge. All the Solutions prepared are given by subject experts keeping in mind the latest syllabus guidelines.

You can refer to Big Ideas Math Answers for Grades K-8 to learn all the chapters and concepts in it effectively. For the sake of your convenience, we have curated the quick links for all the Lessons and Exercises in the Big Ideas Math Book Algebra 1 Answer Key Solving Linear Inequalities. You just need to tap on them to learn about the particular concept in no time.

| -x | = x for x > 0| -x | = -x for x < 0The order of the numbers in the ascending order is:-9, -8, -7, -6, -5, -4 ,-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9We know that,The greater number in the positive integers is the lesser number in the negative integersHence, from the above,-10 < 18 -10 > -18

Question 13.**ABSTRACT REASONING**A number a is to the left of a number b on the number line. How do the numbers -a and -b compare?Answer:It is given that a number a is to the left of a number b on the number line.So,The representation of a and b on the number line is:Hence, from the above number lineWe can conclude that

## Algebra 1 Common Core Answers Chapter 2 Solving Equations Exercise 23

**Chapter 2 Solving Equations Exercise 2.3 1LC**

**Chapter 2 Solving Equations Exercise 2.3 2LC**

**Chapter 2 Solving Equations Exercise 2.3 3LC**

**Chapter 2 Solving Equations Exercise 2.3 4LC**

**Chapter 2 Solving Equations Exercise 2.3 5LC**

**Chapter 2 Solving Equations Exercise 2.3 6LC**

**Chapter 2 Solving Equations Exercise 2.3 7LC**

**Chapter 2 Solving Equations Exercise 2.3 8LC**

**Chapter 2 Solving Equations Exercise 2.3 9LC**

**Chapter 2 Solving Equations Exercise 2.3 10E**

**Chapter 2 Solving Equations Exercise 2.3 11E**

**Chapter 2 Solving Equations Exercise 2.3 12E**

**Chapter 2 Solving Equations Exercise 2.3 13E**

**Chapter 2 Solving Equations Exercise 2.3 14E**

**Chapter 2 Solving Equations Exercise 2.3 15E**

**Chapter 2 Solving Equations Exercise 2.3 16E**

**Chapter 2 Solving Equations Exercise 2.3 17E**

**Chapter 2 Solving Equations Exercise 2.3 18E**

**Chapter 2 Solving Equations Exercise 2.3 19E**

**Chapter 2 Solving Equations Exercise 2.3 20E**

**Chapter 2 Solving Equations Exercise 2.3 21E**

**Chapter 2 Solving Equations Exercise 2.3 22E**

**Chapter 2 Solving Equations Exercise 2.3 23E**

**Chapter 2 Solving Equations Exercise 2.3 24E**

**Chapter 2 Solving Equations Exercise 2.3 25E**

**Chapter 2 Solving Equations Exercise 2.3 26E**

**Chapter 2 Solving Equations Exercise 2.3 27E**

**Chapter 2 Solving Equations Exercise 2.3 28E**

**Chapter 2 Solving Equations Exercise 2.3 29E**

**Chapter 2 Solving Equations Exercise 2.3 30E**

**Chapter 2 Solving Equations Exercise 2.3 31E**

**Chapter 2 Solving Equations Exercise 2.3 32E**

**Chapter 2 Solving Equations Exercise 2.3 33E**

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## Practice Set 23 Algebra 9th Std Maths Part 1 Answers Chapter 2 Real Numbers

Question 1.State the order of the surds given below.Answer:i. 3, ii. 2, iii. 4, iv. 2, v. 3

Question 2.State which of the following are surds Justify. Answer:i. \ is a surd because 51 is a positive rational number, 3 is a positive integer greater than 1 and \ is irrational.

ii. \ is not a surd because= 2, which is not an irrational number.

iii. \ is a surd because 81 is a positive rational number, 5 is a positive integer greater than 1 and \ is irrational.

iv. \ is not a surd because= 16, which is not an irrational number.

v. \ is not a surd because= 4, which is not an irrational number.

vi. \ is a surd because \ is a positive rational number, 2 is a positive integer greater than 1 and \ is irrational.

Question 3.Classify the given pair of surds into like surds and unlike surds. Solution:If the order of the surds and the radicands are same, then the surds are like surds.

Here, the order of 2\ and 5\ is same and their radicands are also same. \ and 5\ are like surds.

Here, the order of 2\ and 5\ is same but their radicands are not. \ and 5\ are unlike surds.

Here, the order of 12\ and 7\ is same and their radicands are also same. 4\ and 7\ are like surds.

Here, the order of 38\ and 6\ is same and their radicands are also same. 19\ and 6\ are like surds.

v. 5\, 7\Here, the order of 5\ and 7\ is same but their radicands are not. 5\ and 7\ are unlike surds.

Here, the order of 55 and 53 is same but their radicands are not. 55 and 75 are unlike surds.

Question 4.

## Solving Linear Inequalities Study Skills: Analyzing Your Errors

**2.12.4 What Did You Learn? **

**Core Vocabulary**

Representing Linear Inequalities, p. 57

**Section 2.2**

Multiplication and Division Properties of Inequality , p. 68Multiplication and Division Properties of Inequality , p. 69

**Section 2.4**Solving Multi-Step Inequalities, p. 74Special Solutions of Linear Inequalities, p. 75

**Mathematical Practices**

Question 1.Explain the meaning of the inequality symbol in your answer to Exercise 47 on page 59. How did you know which symbol to use?Answer:In Exercise 47 on page 59,The inequality symbol we used is: The meaning of is Less than or equal to In Exercise 47,It is given that the Xianren bridge arch is the longest natural arch with a length of 400 feet i.e., there is no arch longer than the Xianren bridge arch and the remaining natural arches are shorter than the Xianren archHence,The lengths of all the arches including the Xianren arch will be represented by the inequality symbol

Question 2.In Exercise 30 on page 66, why is it important to check the reasonableness of your answer in part before answering part ?Answer:In part , it is given that you have to beat your competitor with your score.So,Your score must be greater than your competitorThen only you can solve part .

**Study Skills**

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## Lesson 24 Solving Multi

**Essential Question**How can you solve a multi-step inequality?

**EXPLORATION 1 ****Solving a Multi-Step Inequality ****Work with a partner.**

Use what you already know about solving equations and inequalities to solve each multi-step inequality. Justify each step. Match each inequality with its graph. Use a graphing calculator to check your answer.a. 2x + 3 x + 5b. -2x + 3 > x + 9c. 27 5x + 4xd. -8x + 2x 16 < -5x + 7xe. 3 5x > -3x 6f. -5x 6x 8 8x xAnswer:a. 2x + 3 x + 5b. -2x + 3 > x + 9c. 27 5x + 4xd. -8x + 2x 16 < -5x + 7xe. 3 5x > -3x 6f. -5x 6x 8 8x xThe given graphing calculators are:Now,From the graphing calculators, we can observe that the graph is divided into 4 parts.The first part indicates +xThe second part indicates -xNow,

We can conclude that the solution to the given inequality is x -4The graph F) matches the solution of the given inequality

Question 2.How can you solve a multi-step inequality?Answer:The general procedure for solving multi-step inequality is as follows:a) Clear parenthesis i.e., Brackets on both sides of the inequality and collect like termsb) Addor subtract terms so the variable is on one side and the constant is on another side of the inequality sign

We can conclude that the given inequality has no solution

Question 31.**MODELING WITH MATHEMATICS**Write and solve an inequality that represents how many $20 bills you can withdraw from the account without going below the minimum balance.Answer:

## Solving Inequalities Using Addition Or Subtraction 22 Exercises

**In Exercises 36, tell which number you would add to or subtract from each side of the inequality to solve it.**

Question 1.why is the inequality x 6 equivalent to the inequality x 5 6 5 ?Answer:

We can conclude that the solution to the given inequality is:z > -9The representation of the inequality in the number line is:

**In Exercises 2124, write the sentence as an inequality. Then solve the inequality.**

Question 21.A number plus 8 is greater than 11.Answer:

A number minus 3 is at least -5.Answer:The given worded form is:A number minus 3 is at least -5Let the number be xSo,The representation of the given worded form in the form of inequality is:x 3 -5x 3 + 5 -5 + 5x + 2 0Hence, the solution to the given worded form inequality is:x -2

The difference of a number and 9 is fewer than 4.Answer:

Six is less than or equal to the sum of a number and 15.Answer:The given worded form is:Six is less than or equal to the sum of a number and 15Let the number be xSo,The representation of the given worded form in the form of inequality is:6 x + 156 6 x + 15 60 x + 9We can conclude that the solution to the given worded form of the inequality is:x -9

Question 27.

We can conclude that the solution to the given inequality is:x 1The representation of the inequality in the number line is:

Question 30.**MAKING AN ARGUMENT**In an aerial ski competition, you perform two acrobatic ski jumps. The scores on the two jumps are then added together.

Explanation:

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## Practice A Algebra 1 Answers In 5+ Pages Pptx Powerpoint Explanation

Read 4.2 practice a algebra 1 answers from 6+ different presentation 2 Review Sheet – worked out. 19A4 SpringBoard Algebra 2 Unit 1 Practice 29. Rewrite 2x 8 4 using the Associative. Read also practice and 4.2 practice a algebra 1 answers Algebra 2 practice test with answers pdf algebra 1 practice test with answers pdf algebra practice test with answers algebra 1 practice test with answers algebra nation practice book answers college algebra practice test with answer key algebra 2 practice workbook answer key 61 practice a algebra 1 answers 53 practice a algebra 1.

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Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2 2 Learn Cram S Lear Maths Solutions Quadratics Math Lessons

Slide Topic: Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2 2 Learn Cram S Lear Maths Solutions Quadratics Math Lessons 4.2 Practice A Algebra 1 Answers |

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Open Maharashtra Board Class 10 Maths Solutions Chapter 2 Quadratic Equations Practice Set 2 2 Learn Cram S Lear Maths Solutions Quadratics Math Lessons |

## Solving Linear Inequalities Chapter Test

**Write the sentence as an inequality.**

Question 1.The sum of a number y and 9 is at least -1.Answer:The given worded form is:The sum of a number y and 9 is at least -1Hence,The representation of the given worded form in the form of inequality is:y + 9 -1

A number r is more than 0 or less than or equal to -8.Answer:The given worded form is:A number r is more than 0 or less than or equal to -8Hence,The representation of the given worded form in the form of inequality is:r > 0 or r -8

Question 3.A number k is less than 3 units from 10.Answer:The given worded form is:A number k is less than 3 units from 10Hence,The representation of the given worded form in the form of inequality is:k 10 < 3

**Solve the inequality. Graph the solution, if possible.**

Question 4.\ 5 -9Answer:\ 5 -9\ -9 + 5\ -4

We can conclude that the solution to the given inequality is -3 a 2The representation of the solution of the inequality in the graph is:

Question 9.-5 < 2 h or 6h + 5 > 71Answer:-5 < 2 h or 6h + 5 > 71-5 2 < h or 6h > 71 5-7 < -h or 6h > 667 < h or h > 66 / 6h > 7 or h > 11Hence, from the above,We can conclude that the solution to the given inequality is h > 7 The representation of the solution of the given inequality in the graph is:

Question 15.Let a, b, c, and d be constants. Describe the possible solution sets of the inequality ax + b < cx + d.Answer:

The values of a and b so that the inequality has no solution are:a = 3 and b < 4

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## Solving Compound Inequalities 25 Exercises

**Vocabulary and Core Concept Check**

Question 1.**WRITING**Compare the graph of -6 x -4 with the graph of x -6 or x -4.Answer:

**WHICH ONE do DOESNT BELONG?**Which compound inequality does not belong with the other three? Explain your reasoning.Answer:a. a > 4 or a < -3b. a< -2 or a > 8c. a > 7 or a < -5d. a < 6 or a > -9Now,Represent all the inequalities in the graphSo,

From the above graph,We can observe thatThe first marked line started from 4 including 4 and continued till the end of the left end of the graphThe second marked line started from 6 excluding 6 and continued till the end of the right end of the graphHence,The representation of the given graph in the form of inequality is:x 4 or x > 6

**In Exercises 710, write the sentence as an inequality. Graph the inequality.**

Question 7.A number p is less than 6 and greater than 2.Answer:

A number n is less than or equal to -7 or greater than 12.Answer:The given worded form is:A number n is less than or equal to -7 or greater than 12Hence,The representation of the given worded form in the form of inequality is:n -7 or n > 12The representation of the inequalities in the graph is:

Question 9.A number m is more than -7\ or at most -10.Answer:

Question 11.**MODELING WITH MATHEMATICS**Slitsnails are large mollusks that live in deep waters. They have been found in the range of elevations shown. Write and graph a compound inequality that represents this range.Answer:

**In Exercises 1320, solve the inequality. Graph the solution.**