Question

Solve each inequality. Graph the solution set on a number line.

$\left|4k-8\right|<20$.

Short answer

The solution of the given absolute inequality is $-3<k<7$.

Step-by-step solution

-Write the inequalities 

A For all real numbers a, b and $b>0$; it is true that if $\left|a\right|<b$then $-b<a<b$. The given absolute inequality is$\left|4k-8\right|<20$.

– Apply the definition of an absolute compound inequality

Use the definition of absolute value inequality and write the compound inequality as follows:

$\begin{array}{c}|4k-8|<20\\ -20<4k-8<20\\ -20+8<4k-8+8<20+8\\ -12<4k<28\end{array}$

Therefore, the solution of the given absolute inequality is $-3<k<7$

– Graph of the solution set 

The graph for the inequality $-3<k<7$is as shown below