Q65. - Algebra 2

Question

Solve each equation. Check your solution.

 

$65.\left|w+3\right|=12$

Step-by-Step Solution

Answer

The solutions of the equation are $w=9$ and $w=-15$.

Step-1 – Apply the concept of Absolute value

On real number line, the distance of a number from 0 is the absolute value. It is always nonnegative.

The absolute value of a function is expressed as, if x is a real number then absolute value of x is defined as.

$\left|x\right|=x$ when x is greater than or equal to 0 . In other words, the absolute value of x is x when x is either positive or zero.

$\left|x\right|=-x$ when x is less than 0 . In other words, the absolute value of x is opposite of x when x is negative.

Step-2 –Example of Absolute value

The absolute value of 5 is expressed as $\left|5\right|=5$ and of $-5$ is expressed as $\left|-5\right|=5$

Step-3 – Simplify the equation

Consider the provided equation.

$\left|w+3\right|=12$

Recall the concept of absolute value and apply it.

Case 1. $w+3=12$

Subtract 3 from both the sides.

$\begin{array}{c}w+3-3=12-3\\ w=9\end{array}$

Case 2. $w+3=-12$

Subtract 3 from both the sides.

$\begin{array}{c}w+3-3=-12-3\\ w=-15\end{array}$

Therefore, there are two possible solutions for the equation $\left|w+3\right|=12$ that are $w=9$ and $w=-15$.

Step-4 – Verify the solutions

Substitute the value $w=9$ in the equation $\left|w+3\right|=12$.

$\begin{array}{c}\left|9+3\right|=12\\ \left|12\right|=12\\ 12=12\end{array}$

Since, this is true so the value $w=9$ satisfy the equation $\left|w+3\right|=12$.

Substitute the value $w=-15$ in the equation $\left|w+3\right|=12$.

$\begin{array}{c}\left|-15+3\right|=12\\ \left|-12\right|=12\\ 12=12\end{array}$

Since, this is true so the value $w=-15$ satisfy the equation $\left|w+3\right|=12$.

Thus, the solution set is $\left\{-15,9\right\}$.

Hence, the solutions of the equation are $w=-15$ and $w=9$.