Question

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

$-\left|5a+c\right|+\left|3y+2z\right|$

Short answer

The expression $-\left|5a+c\right|+\left|3y+2z\right|$ is equal to -7.4.

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 $-\left|5a+c\right|+\left|3y+2z\right|$ substitute -2 for a, -3 for b, 2 for c, 2.1 for x, 3 for y and -4.2 for z.

$-\left|5a+c\right|+\left|3y+2z\right|=-\left|5\times \left(-2\right)+2\right|+\left|3\times 3+2\times \left(-4.2\right)\right|$

Step-3. Simplify the expression.

Solve the expression as per order of operations.

$$\begin{gathered} -\left|5a+c\right|+\left|3y+2z\right|=-\left|5\times \left(-2\right)+2\right|+\left|3\times 3+2\times \left(-4.2\right)\right| \\ =-\left|-10+2\right|+\left|3\times 3-8.4\right| \\ =-\left|-8\right|+\left|9-8.4\right| \\ =-\left|-8\right|+\left|0.6\right| \\ =-8+0.6 \\ =-7.4 \end{gathered}$$

Therefore, the value expression is $-7.4$.