Question

Evaluate each expression if $a=-2,b=-3,c=2$, $x=2.1,y=3$, and $z=-4.2$.

$-3\left|z\right|+2\left(a+y\right)$

Short answer

The expression$-3\left|z\right|+2\left(a+y\right)$ is equal to $-10.6$.

Step-by-step solution

Step-1. Define absolute value expression.

Absolute values define an upper and lower range in which a value must lie.

Step-2. Substitute the variables.

In order to evaluate the expression $-3\left|z\right|+2\left(a+y\right)$ substitute -2 for a, -3 for b, 2 for c, 2.1 for x, 3 for y and -4.2 for z.

$-3\left|z\right|+2\left(a+y\right)=-3\left|-4.2\right|+2\left(-2+3\right)$

Step-3. Simplify the expression.

Solve the expression as per order of operations.

$$\begin{gathered} -3\left|z\right|+2\left(a+y\right)=-3\left|-4.2\right|+2\left(-2+3\right) \\ =-3\times \left|-4.2\right|+2\left(1\right) \\ =-3\times 4.2+2 \\ =-12.6+2 \\ =-10.6 \end{gathered}$$

Therefore, the value expression is $-10.6$.