Question

Solve the compound inequality. Write the answer in interval notation. $$- 1 < \frac { 3 - x } { 2 } \leq 0$$

Name: Problem 70, Chapter 1: Intermediate Algebra
Uploaded: 2020-07-13T10:32:54-08:00
Duration: 1 min 6 s
Channel: Ankit Gupta
Description: Solve the compound inequality. Write the answer in interval notation. - 1 < ( 3 - x )/( 2 ) ≤0

   Solve the compound inequality. Write the answer in interval notation.
$$- 1 < \frac { 3 - x } { 2 } \leq 0$$

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 1, Problem 70

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Solved by Expert Ankit Gupta

07/13/2020

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This gives us: $$-2 < 3 - x \leq 0$$ Show more…

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Solve the compound inequality. Write the answer in interval notation. $$- 1 < \frac { 3 - x } { 2 } \leq 0$$

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Key Concepts

Compound Inequality

A compound inequality involves two or more inequalities that must be satisfied at the same time. It typically requires finding the intersection of solution sets since the variable must meet all conditions simultaneously.

Inequality Manipulation

Solving inequalities involves applying algebraic operations such as addition, subtraction, multiplication, or division to isolate the variable. Special caution is needed when multiplying or dividing by negative numbers, as the direction of the inequality sign must be reversed.

Interval Notation

Interval notation is a concise way to represent sets of numbers along a number line. It uses brackets to indicate whether endpoints are included (closed interval) or excluded (open interval), offering a clear depiction of the range of solutions.

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