Question

Evaluate the expression.

$\left|\mathbf{5}\mathbf{-}\left|\mathbf{10}\mathbf{-}\left|-4\right|\right|\right|$

Short answer

Answer is 1.

Step-by-step solution

Step 1. Understanding the concept of Absolute value.

In the given expression concept of absolute value is required. Here $\left|\text{-4}\right|\text{=4}$

Absolute value is how much a number is distant from the origin without taking in consideration the signs associated with it.

Step 2. Replacing -4 with 4.

Thus, the expression becomes

$\left|5-\left|10-4\right|\right|$

Step 3. Again we shall find the absolute value to determine the answer.

$\begin{array}{c}\left|\text{5-}\left|\text{10-4}\right|\right|\text{=}\left|\text{5-6}\right|\\ \left|\text{5-6}\right|\text{=}\left|\text{-1}\right|\\ \left|\text{-1}\right|\text{=1}\end{array}$