Chapter 11.3, Problem 1MRE

To determine

To calculate:

Given inequality and graph the solution.

Answer to Problem 1MRE

The solution of the inequality is $x<-2$ or $x<7$ .

Explanation of Solution

Given information:

Equation:

  $\left|2x-5\right|>9$

Formula used:

Absolute rule:

If $\left|u\right|>a,a>0$ then $u<-a$ or $u>a$

Calculation:

Consider the equation $\left|2x-5\right|>9$

Then use the absolute rule, so if $\left|u\right|>a,a>0$ then $u<-a$ or $u>a$ then,

  $2x-5>-9$ or $2x-5>9$

  $2x-5<-9:x<-2$

Now combine the intervals.

  $x<-2$ or $x<7$

Now, draw the graph.

The following graph shoes the equation $\left|2x-5\right|>9$ .