Question

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

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

Short answer

The expression$4a-\left|3b+2c\right|$ is equal to -13.

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

$4a-\left|3b+2c\right|=4\times \left(-2\right)-\left|3\times \left(-3\right)+2\times 2\right|$

Step-3. Simplify the expression.

Solve the expression as per order of operations.

$$\begin{gathered} 4a-\left|3b+2c\right|=4\times \left(-2\right)-\left|3\times \left(-3\right)+2\times 2\right| \\ =-8-\left|3\times \left(-3\right)+2\times 2\right| \\ =-8-\left|-9+4\right| \\ =-8-\left|-5\right| \\ =-8-5 \\ =-13 \end{gathered}$$

Therefore, the value expression is -13.