Q21. - Algebra 1

Question

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

$-4\left|c-3\right|+2\left|z-a\right|$

Step-by-Step Solution

Answer

The expression $-4\left|c-3\right|+2\left|z-a\right|$ is equal to $0.4$.

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 $-4\left|c-3\right|+2\left|z-a\right|$ substitute -2 for a, -3 for b, 2 for c, 2.1 for x, 3 for y and -4.2 for z.

$-4\left|c-3\right|+2\left|z-a\right|=-4\left|2-3\right|+2\left|-4.2-\left(-2\right)\right|$

Step-3. Simplify the expression.

Solve the expression as per order of operations.

$$\begin{gathered} -4\left|c-3\right|+2\left|z-a\right|=-4\left|2-3\right|+2\left|-4.2-\left(-2\right)\right| \\ =-4\left|2-3\right|+2\left|-4.2+2\right| \\ =-4\left|-1\right|+2\left|-2.2\right| \\ =-4\times 1+2\times 2.2 \\ =-4+4.4 \\ =0.4 \end{gathered}$$

Therefore, the value expression is $0.4$.