Question

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

$\left|-2p+m\right|-3n$

Short answer

The value of the expression is $4$.

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$\left|-2p+m\right|-3n$and$m=-8,n=4,$plugging these values:

We get:

localid="1643037484011" $\begin{array}{l}|-2p+m|-3n\\ =|-2\times \left(-12\right)-8|-3\times 4\end{array}$

Step 2. Simplify the expression.

$\begin{array}{l}|-2\times \left(-12\right)-8|-3\times 4\\ =|24-8|-12\\ =\left|16\right|-12\end{array}$

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 $\left|16\right|-12$, now using definition of absolute value function we get:

role="math" localid="1643037396602" $\begin{array}{l}\left|16\right|-12\\ =16-12\\ =4\end{array}$

Thus, the value of the expression is $4$.