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

Question

asked Jul 12, 2023 78.3k views

1 Answer

Coolest · Answer 1 · 2023-07-17T07:26:34+0000

Given:

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:

And,

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

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

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

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

Therefore, the answer is A. The solution set is

$\lbrace-(6)/(7),(12)/(7)\rbrace$