Q69. - Algebra 2

Question

Solve each equation. Check the solution.

 

$\left|5\text{y}-8\right|=12$

Step-by-Step Solution

Answer

The value of $\text{y}$ is $\mathbf{4}$ and $-\mathbf{0}.\mathbf{8}$.

Step 1 - State the definition of absolute value.

The distance of a number from 0 in the number line is called the absolute value and since distance cannot be negative so absolute value is always positive.

Step 2 - Solve the inequality.

If x is a number, then absolute value of x is written as $\left|x\right|$.

 

Here, the inequality is:

 

$\left|5y-8\right|=12$

 

Case 1: 

 

$\begin{array}{c}a=b\\ 5y-8=12\\ 5y-8+8=12+8\\ 5y=20\\ y=4\end{array}$

 

Or Case 2:

 

$\begin{array}{c}a=-b\\ 5y-8=-12\\ 5y-8+8=-12+8\\ 5y=-4\\ y=-0.8\end{array}$

 

The solution is $4$ and $-0.8$

Step 3 - Check the solution.

For case 1: $y=4$.

 

Check:

 

$\begin{array}{r}\left|5y-8\right|=12\\ \left|\left(5\times 4\right)-8\right|=12\\ \left|20-8\right|=12\\ \left|12\right|=12\\ 12=12\end{array}$

 

Thus, it is correct.

 

For case 2: $y=-0.8$.

 

Check:

 

$\begin{array}{r}\left|5y-8\right|=12\\ \left|\left(5\times -0.8\right)-8\right|=12\\ \left|-4-8\right|=12\\ \left|-12\right|=12\\ 12=12\end{array}$

 

Thus, it is also correct.

Step 4 - State the conclusion.

Therefore, the solution set for y is $\left\{4,-0.8\right\}$.