Question

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

$\left|2x-z\right|+6b$

Short answer

The expression$\left|2x-z\right|+6b$ is equal to $-9.6$.

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 $\left|2x-z\right|+6b$ substitute -2 for a, -3 for b, 2 for c, 2.1 for x, 3 for y and -4.2 for z.

$\left|2x-z\right|+6b=\left|2\times 2.1-\left(-4.2\right)\right|+6\times \left(-3\right)$

Step-3. Simplify the expression.

Solve the expression as per order of operations.

$$\begin{gathered} \left|2x-z\right|+6b=\left|2\times 2.1-\left(-4.2\right)\right|+6\times \left(-3\right) \\ =\left|2\times 2.1+4.2\right|+6\times \left(-3\right) \\ =\left|2\times 2.1+4.2\right|-18 \\ =\left|4.2+4.2\right|-18 \\ =\left|8.4\right|-18 \\ =8.4-18 \\ =-9.6 \end{gathered}$$

Therefore, the value expression is $-9.6$.