Question

Simplify: $9-\left|8-4\left(7-5\right)\right|$.

Short answer

The simplified value is 9.

Step-by-step solution

Step 1. Given Information. 

Consider the given expression,

$9-\left|8-4\left(7-5\right)\right|$

Step 2. Perform Subtraction. 

Start with the innermost grouping symbol, which is parentheses in this case. Subtract 5 from 7 inside the parentheses.

$9-\left|8-4\left(2\right)\right|$

Step 3. Perform Multiplication. 

Multiply 4 by 2 within the absolute value bars.

$9-\left|8-8\right|$

Step 4. Perform Subtraction. 

Subtract 8 from 8 within the absolute value bars.

$9-\left|0\right|$

Step 5. Simplification.

The distance of 0 from itself is 0, so the absolute value of 0 is 0. This implies that $\left|0\right|=0$.

Substitute 0 for $\left|0\right|$in the obtained expression and subtract.

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

Step 6. Conclusion.

The simplified value of $9-\left|8-4\left(7-5\right)\right|$is 9.