Q50. - Algebra 1

Question

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

$4\left|7m+3p\right|+4n$ 

Step-by-Step Solution

Answer

The value of the expression is $384$.

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 $4\left|7m+3p\right|+4n$ and $m=-8,n=4,p=-12$, plugging these values:

We get:

$\begin{array}{l} 4|7m+3p|+4n\\ =4|7\times \left(-8\right)+3\times \left(-12\right)|+4\times 4\end{array}$

Step 2. Simplify the expression.

$\begin{array}{l}4|7\times \left(-8\right)+3\times \left(-12\right)|+4\times 4\\ 4|-56+-36|+16\\ 4|-92|+16\end{array}$

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 $4|-92|+16$, now using definition of absolute value function we get:

$\begin{array}{l} 4|-92|+16\\ =4\times 92+16\\ =368+16\\ =384\end{array}$

Thus, the value of the expression is $384$.