Question

Evaluate the expression when $x=-4$.

$\left|x\right|-1$

Short answer

The value of the expressionis 3.

Step-by-step solution

Step 1. Absolute value of a number

Absolute value of any positive or negative number is always positive and equal to the magnitude of the number. The absolute value of a number N is denoted by $\left|N\right|$.

For example, the absolute value of 3 is denoted by $\left|3\right|$and is equal to 3.

And the absolute value of $-4$is denoted by $\left|-4\right|$and is equal to 4.

Step 2. Apply the concept of addition and subtraction

Two numbers with similar signs get added and the resulting number carries the similar sign.

Two numbers with opposite signs get subtracted and the resulting number carries the sign of the larger number.

Step-3 – Evaluate the expression

To evaluate the value of the expression $\left|x\right|-1$, substitute $-4$ for x and simplify further as shown below,

$\begin{array}{c}\left|x\right|-1=\left|-4\right|-1\\ =4-1\\ =3\end{array}$

Thus, the value of the given expression is 3.