Question

In the following exercise, simplify each expressions.

$25-\left[10-\left(3-12\right)\right]$

Short answer

The simplified value is 6.

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 12 with 3 inside the parentheses.

$\begin{array}{rcl}25-\left[10-\left(3-12\right)\right]& =& 25-\left[10-\left(-9\right)\right]\end{array}$

Step 3. Simplification inside brackets.

Add the opposite of the opposite of 9 with 10 inside the brackets.

$\begin{array}{rcl}25-\left[10-\left(-9\right)\right]& =& 25-\left[10+9\right]\\ & =& 25-\left[19\right]\end{array}$

Step 4. Calculation.

Add the opposite of 19 with 25.

$\begin{array}{rcl}25-\left[19\right]& =& 25-19\\ & =& 6\end{array}$

Step 5. Conclusion.

The simplified value of the given expression is 6.