Question

Solve each expression if $x=-2,y=6,\text{and}z=4$. (Lesson 2-5)

role="math" $12-\left|z+9\right|$

Short answer

The value of the expression is$-1$

Step-by-step solution

Step-1. Use the definition of absolute value function.

The absolute value or modulus of a real number x, denoted |x| is the non-negative value of x without regard to its sign.

Absolute value refers to a point's distance from zero or origin on the number line, regardless of the direction.

Step-2. Plug values and Simplify.

We are given the expressions: $12-|z+9|$

Plugging the values $x=-2,y=6,\text{and}z=4$and simplifying as shown we get:

$\begin{array}{l}=12-\left|z+9\right|\\ =12-\left|4+9\right|\\ =12-\left|13\right|\\ =12-13\\ =-1\end{array}$

Thus the value of the expression is $-1$.