Question

Solve each expression if $x=-2,y=6,\text{and}z=4$

$\left|y+x\right|-z+4$

Short answer

The value of the expression is$4$

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: $|y+x|-z+4$

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

$\begin{array}{l}=\left|y+x\right|-z+4\\ =\left|6+\left(-2\right)\right|-4+4\\ =\left|6-2\right|\\ =\left|4\right|\\ =4\end{array}$

Thus the value of the expression is $4$.