Question

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

$|2x+z|+2y$

Short answer

The expression$|2x+z|+2y$ is equal to 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 $|2x+z|+2y$ substitute -2 for a, -3 for b, 2 for c, 2.1 for x, 3 for y and -4.2 for z.

$|2x+z|+2y=|2\times 2.1+\left(-4.2\right)|+2\times 3$

Step-3. Simplify the expression.

Solve the expression as per order of operations.

$$\begin{gathered} \left|2x+z\right|+2y=\left|2\times 2.1+\left(-4.2\right)\right|+2\times 3 \\ =\left|2\times 2.1-4.2\right|+6 \\ =\left|4.2-4.2\right|+6 \\ =\left|0\right|+6 \\ =6 \end{gathered}$$

Therefore, the value expression is 6.