Question

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

$-3\left|6n-2p\right|$

Short answer

The value of the expression is $-144$.

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 $-3\left|6n-2p\right|$and $m=-8,n=4,$, plugging these values:

We get:

$\begin{array}{l}-3|6n-2p|\\ =-3|6\times 4-2\left(-12\right)|\end{array}$

Step 2. Simplify the expression.

$\begin{array}{l}-3|6\times 4-2\left(-12\right)|\\ =-3|24+24|\\ =-3\left|48\right|\end{array}$

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 is$x$ 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 $-3\left|48\right|$, now using definition of absolute value function we get:

$\begin{array}{l}-3\left|48\right|\\ =-3\times 48\\ =-144\end{array}$

Thus, the value of the expression is $-144$.