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Solving Inequalities Study Guide, Assignments of Mathematics

Mathematics

This study guide focuses on solving inequalities, covering topics such as dividing or multiplying inequalities, solving for variables, and understanding special cases. It also explains compound inequalities, including 'and' and 'or' types, and absolute value inequalities. The guide provides step-by-step instructions and examples to help students understand and solve various types of inequalities, including absolute value inequalities. It includes fill-in-the-blank exercises to reinforce key concepts and problem-solving skills, making it a useful resource for high school students studying algebra.

Typology: Assignments

2024/2025

Uploaded on 09/27/2025

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Use the questions below to keep track of key concepts from this

lesson's study activity.

Page 2:

Whenever you divide or multiply both sides of an inequality by a

_______________ number, you need to _______________ the inequality

symbol.

Solve each inequality for

–3

≤ 6

Page 4:

Fill in the right column to solve the inequality.

Step –4

– 3 < 7 + 6

Eliminate the variable term on the

right side of the equation.

Partial preview of the text

Download Solving Inequalities Study Guide and more Assignments Mathematics in PDF only on Docsity!

Use the questions below to keep track of key concepts from this lesson's study activity. Page 2: Whenever you divide or multiply both sides of an inequality by a _______________ number, you need to _______________ the inequality symbol.

Solve each inequality for x.

–3 x ≤ 6

Page 4: Fill in the right column to solve the inequality.

Step –4 x – 3 < 7 + 6 x

Eliminate the variable term on the right side of the equation.

Simplify. Isolate the variable term on one side of the equation. Simplify. Isolate the variable on one side of the equation. Simplify. Page 5: Fill in the blanks to describe two special cases for solving inequalities with variables on both sides of the inequality sign. a. When solving results in an inequality that is true, such as 7 > 3, the solution of the inequality is _________________________. b. When solving results in an inequality that is false, such as 2 ≤ –5, the inequality has _______________ solution. Page 7: Fill in the blanks to describe inequalities with two parts. a. A _______________ inequality is a sentence that joins two inequalities

with the word and or or.

b. Graph the solution to or on the number line below. Pages 12 – 14:

Fill in the blanks to describe less than absolute value inequalities.

a. To solve any less than absolute value inequality, you can write and

solve a related [ or/ and] compound inequality.

b. To solve | x| < a, where x is any algebraic expression and a is any

constant:

x [< / >] – a and x [< / >] a. This can also be written as the single

inequality _______________.

c. The graph of | x| < a is the [union/intersection] of the graphs of the

individual inequalities and shows numbers that are solutions of [both/either] of the inequalities.

d. The graph of | x| < a is [A/B].

A.

B.

Fill in the right column to solve and graph the absolute value inequality.

Step | x + 3| < 2

Write an and

compound inequality.

and

Solve each inequality separately. Write the solution as a single inequality. Graph the solution. Pages 15 – 17:

Fill in the blanks to describe greater than absolute value inequalities.

a. To solve any greater than absolute value inequality, you can write

and solve a related [ or/ and] compound inequality.

b. To solve | x| > a, where x is any algebraic expression and a is any