Q18. - Algebra 1

Question

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

$3\left|3b-8c\right|-3$

Step-by-Step Solution

Answer

The expression $3\left|3b-8c\right|-3$ is equal to 72.

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 $3\left|3b-8c\right|-3$ substitute -2 for a, -3 for b, 2 for c, 2.1 for x, 3 for y and  for z.

$3\left|3b-8c\right|-3=3\left|3\left(-3\right)-8\times 2\right|-3$

Step-3. Simplify the expression.

Solve the expression as per order of operations.

$$\begin{gathered} 3\left|3b-8c\right|-3=3\left|3\left(-3\right)-8\times 2\right|-3 \\ =3\left|-9-8\times 2\right|-3 \\ =3\left|-9-16\right|-3 \\ =3\left|-25\right|-3 \\ =3\times 25-3 \\ =75-3 \\ =72 \end{gathered}$$

Therefore, the value expression is 72.