Chapter 12.1, Problem 47WE

To determine

To solve: The equation $5{\left(6x-1\right)}^2=5$ .

Answer to Problem 47WE

The solution set is $\left(\frac{1}{3},0\right)$ .

Explanation of Solution

Given information:

The given equation $5{\left(6x-1\right)}^2=5$ .

Calculation:

  $\begin{array}{l}\Rightarrow 5{\left(6x-1\right)}^2=5\\ \Rightarrow \frac{5{\left(6x-1\right)}^2}{5}=\frac{5}{5}\end{array}$

(Divide by 5 on both sides)

  $\begin{array}{l}\Rightarrow {\left(6x-1\right)}^2=1\\ \Rightarrow 6x-1=\pm \sqrt{1}\\ \Rightarrow 6x-1+1=\pm 1+1\end{array}$

(Adding 1 on both sides)

  $\begin{array}{l}\Rightarrow 6x=\pm 1+1\\ \Rightarrow \frac{6x}{6}=\frac{\pm 1+1}{6}\end{array}$

(Divide by 6 on both sides)

  $\begin{array}{l}\Rightarrow x=\frac{\pm 1+1}{6}\\ \Rightarrow x=\frac{1}{3};x=0\end{array}$

Therefore, the solution set is $\left(\frac{1}{3},0\right)$ .