Question

Which of the following are solutions to |x-1|= 5x + 2? Check all that apply.
A: x=3/4
B: x=3/4, 1/6
C: x= -1/6
D: x= 1/6

Answer 1

Answer:

The solution of |x-1| = 5x + 2 is $x = \frac{-1}{6}$ and option c is correct.

Solution:

Given, equation is |x-1|= 5x + 2

We have to find the value of x  

Now, |x-1|= 5x + 2  

Because mod becomes "±" when shifted to opposite side of “=”

x – 1 = ±(5x+2)    

x – 1 = 5x + 2 or x – 1 = -(5x + 2)

$\begin{array}{l}{\rightarrow 5 x-x=-1-2 \text { or } x-1=-5 x-2} \\\\ {\rightarrow 4 x=-3 \text { or } 5 x+x=1-2} \\\\ {\rightarrow 4 x=-3 \text { or } 6 x=-1} \\\\ {\rightarrow x=\frac{-3}{4} \text { or } x=\frac{-1}{6}} \\\\ {\rightarrow x=\frac{-3}{4} \text { or } \frac{-1}{6}}\end{array}$

In options we have only $x = \frac{-1}{6}$

Hence, the value of x is $\frac{-1}{6}$ and option c is correct