Question

Solve the following Let f(x) = | 1-7x /3 | find all of x for which f (x) = 3

Answer 1

Given:

$f(x)=|\frac{1-7x}{3}|$

To find the values of x when f(x)=3, we apply below absolute rule:

If |u|=a, a>0 then, u=a or u= -a

Based on the above rule, our equations would be:

$1-\frac{7x}{3}=3$

And,

$1-\frac{7x}{3}=-3$

Next, we find x for 1-7x/3=3:

$\begin{gathered} 1-\frac{7x}{3}=3 \\ \text{Simplify and rearrange:} \\ \frac{7x}{3}=1-3 \\ \frac{7x}{3}=-2 \\ 7x=-2(3) \\ 7x=-6 \\ x=-\frac{6}{7} \end{gathered}$

Then, we find x for 1-7x/3=-3:

$\begin{gathered} 1-\frac{7x}{3}=-3 \\ \text{Simplify and rearrange} \\ \frac{7x}{3}=1+3 \\ \frac{7x}{3}=4 \\ 7x=4(3) \\ 7x=12 \\ x=\frac{12}{7} \end{gathered}$

Therefore, the answer is A. The solution set is

$\lbrace-\frac{6}{7},\frac{12}{7}\rbrace$