Question

In the following exercises, simplify.

$|17-8|-|13-4|$

Short answer

The simplified value is 0.

Step-by-step solution

Step 1. Concept Used. 

The absolute value of a number $x$ is equal to the distance between$x$ and 0 on the number line.

Step 2. Perform Subtraction.

Subtract 8 from 17 and 4 from 13 within the absolute value bars.

$\left|9\right|-\left|9\right|$

Step 3. Simplify the absolute value bars.

The distance of 8 from 0 is 8 units. So, $\left|9\right|=9$.

$\begin{array}{rcl}\left|9\right|-\left|9\right|& =& 9-9\\ & =& 0\end{array}$

Step 4. Conclusion. 

The simplified value of the expression$\left|17-8\right|-\left|13-4\right|$is 0.