Chapter 1.5, Problem 52E

To determine

To solve the equation:

  $\left|3y-12\right|-7=2$

And also graph the solution.

Answer to Problem 52E

  $y=\frac{20}{3},\text{ and }y=1$

  

Explanation of Solution

Given:

  $\left|3y-12\right|-7=2$

Concept Used:

• Property of absolute value:

1. $\left|a\right|=a;\text{ if }a\ge 0$

2. $\left|a\right|=-a;\text{ if }a<0$

• To solve $\left|ax+b\right|=c,c\ge 0$, solve the related equations:

  $ax+b=c,\text{ or }ax+b=-c$

Calculation:

In order to solve the equation:

  $\left|3y-12\right|-7=2$

First, simplify this equation, as:

  $\begin{array}{c}\left|3y-12\right|-7=2\\ \Rightarrow \left|3y-12\right|=2+7\\ \Rightarrow \left|3y-12\right|=9\end{array}$

Form the related equations:

  $3y-12=9,\text{ and }3y-12=-9$

Now, solve above equations add 12 each sides, as

  $\begin{array}{c}3y-12+12=9+12,\text{ and }3y-12+12=-9+12\\ \Rightarrow 3y=20,\text{ and }3y=3\end{array}$

Now, to find value of y in each case divide each side by 4, as

  $\begin{array}{c}3y=20,\text{ and }3y=3\\ \Rightarrow \frac{3y}{3}=\frac{20}{3},\text{ and }\frac{3y}{3}=\frac{3}{3}\\ \Rightarrow y=\frac{20}{3},\text{ and }y=1\end{array}$

Thus, solutions for given equation are $y=\frac{20}{3},\text{ and }y=1$ .

Now, represent the solution of the given equation by representing points 1, and $\frac{20}{3}$ on the number line using a graphing tool.