Question

Evaluate each expression if $m=-8,n=4,$and $p=-12$.

$\left|3m-n\right|$

Short answer

The value of the expression is $28$.

Step-by-step solution

Step 1. Plug the values of the variables.

A variable is a letter or a literal used to signify an unknown quantity.

We are given the expression$\left|3m-n\right|$ and$m=-8,n=4,$ plugging these values:

We get:

$|3\left(-8\right)-4|$

Step 2. Simplify the expression.

$\begin{array}{l}|3\left(-8\right)-4|\\ |-24-4|\\ |-28|\end{array}$

Step 3. Apply the definition of absolute function.

The absolute value or modulus of a real number x, denoted $\left|x\right|$, it is the non-negative value of $x$without regard to its sign.

$\left|x\right|=x$if$x$ is positive,

$\left|x\right|=-x$if$x$ is negative,

$\left|0\right|=0$.

For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5.

We have the expression$|-28|$ now using definition of absolute value function we get:

$|-28|=28$

Thus, the value of the expression is $28$.