Question

In the following exercise, simplify each expressions.

$32-\left[5-\left(15-20\right)\right]$

Short answer

The simplified value is 22.

Step-by-step solution

Step 1. Concept Used.

According to subtraction property, the subtraction of a number is equal to the addition of its opposite. This can be expressed as follows.

$a-b=a+\left(-b\right)$

Step 2. Simplification inside parentheses.

Add the opposite of 20 with 15 inside the parentheses.

$32-\left[5-\left(15-20\right)\right]=32-\left[5-\left(-5\right)\right]$

Step 3. Simplification inside brackets.

Add the opposite of the opposite of 5 with 5 inside the brackets.

$\begin{array}{rcl}32-\left[5-\left(-5\right)\right]& =& 32-\left[5+5\right]\\ & =& 32-\left[10\right]\end{array}$

Step 4. Calculation.

Add the opposite of 10 with 32.

$\begin{array}{rcl}32-\left[10\right]& =& 32-10\\ & =& 22\end{array}$

Step 5. Conclusion.

The simplified value of the given expression is 22.