Chapter 4.7, Problem 55STP

To determine

To find: the solution set of the inequality as mentioned in the problem.

Answer to Problem 55STP

The solution set of the inequality $\left|4x-1\right|<9$ is $\left\{x|-2<x<2.5\right\}$ .

Explanation of Solution

Given information:

The inequality mentioned in the problem is $\left|4x-1\right|<9$ .

Formula used:

The modulus formula if $\left|a\right|<x\Rightarrow -x<a<x$ .

Calculation:

Consider the inequality mentioned is $\left|4x-1\right|<9$ .

Recall that if $\left|a\right|<x\Rightarrow -x<a<x$ .

Therefore $\left|4x-1\right|<9$ $\Rightarrow -9<4x-1<9$ .

Therefore $-9<4x-1<9\Rightarrow -9+1<4x<9+1\Rightarrow -8<4x<10\Rightarrow -2<x<2.5$ .

Therefore the solution set of the inequality $\left|4x-1\right|<9$ is $\left\{x|-2<x<2.5\right\}$ .