Question

In the following exercises, simplify.

$\left|15-7\right|-\left|14-6\right|$

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 7 from 15 and 6 from 14 within the absolute value bars.

$\left|8\right|-\left|8\right|$

Step 3. Simplify the absolute value bars.

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

$\begin{array}{rcl}\left|8\right|-\left|8\right|& =& 8-8\\ & =& 0\end{array}$

Step 4. Conclusion.

The simplified value of $\left|15-7\right|-\left|14-6\right|$is 0.