step 1 Okay, so we have the opposite value. So we have two solutions. 3x minus 4 is greater than 11. Or

Question

$$\text { Solve: }|3 x-4|>11$$

Name: Problem 134, Chapter 10: Introductory and Intermediate Algebra for College Students 4th
Uploaded: 2020-06-06T18:23:14-08:00
Duration: 38 s
Channel: Amy Jiang
Description: Solve: |3 x-4|>11

   $$\text { Solve: }|3 x-4|>11$$

Introductory and Intermediate Algebra for College Students 4th

Robert Blitzer 4th Edition

Chapter 10, Problem 134

Instant Answer

Solved by Expert Amy Jiang

06/06/2020

Step 1

This means that $3x - 4$ is either greater than 11 or less than -11. So we can write this as two separate inequalities: $3x - 4 > 11$ and $3x - 4 < -11$. Show more…

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$$\text { Solve: }|3 x-4|>11$$

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Key Concepts

Absolute Value

Absolute value represents the distance of a number or expression from zero on the number line, regardless of its sign. It is a fundamental concept in mathematics that helps in measuring how far a value is from zero, thereby ignoring negative signs.

Inequalities

Inequalities are mathematical statements that compare two expressions using symbols like >, <, ?, or ?. They are used to describe a range or interval of values that satisfy a certain condition, rather than a single fixed value.

Case Analysis for Absolute Value Inequalities

When solving inequalities that involve absolute values, one must consider the definition of absolute value and split the inequality into separate cases depending on whether the expression inside is positive or negative. This method helps in accurately determining the range of values that satisfy the inequality.

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