Question

In the following exercise, simplify.

$13-2\left|11-2\left(5-2\right)\right|$

Short answer

The simplified value is 3.

Step-by-step solution

Step 1. Simplification inside parentheses.   

Subtract 2 from 5 inside the parentheses.

$13-2\left|11-2\left(5-2\right)\right|=13-2\left|11-2\left(3\right)\right|$

Step 2. Multiplication.  

Multiply 2 by 3.

$13-2\left|11-2\left(3\right)\right|=13-2\left|11-6\right|$

Step 3. Simplification.

• Simplify inside the absolute value bars.
• Take the absolute value and multiply it with 2.
• Subtract the value from 13.

$\begin{array}{rcl}13-2\left|11-6\right|& =& 13-2\left|5\right|\\ & =& 13-2\left(5\right)\\ & =& 13-10\\ & =& 3\end{array}$

Step 4. Conclusion.

The simplified value of the given expression is 3.