Q48. - Algebra 1

Question

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

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

Step-by-Step Solution

Answer

The value of the expression is $4$.

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:

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

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:

$\begin{array}{l}\left|16\right|-12\\ =16-12\\ =4\end{array}$

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