Question

Solve the equation: $|4x-2|=8x-12$

• A. $\frac{5}{2}$
• B. $\frac{7}{6}$
• C. $\frac{3}{2}$
• D. $\frac{1}{2}$

Answer 1

Answer: (A), (B)

The correct options are
A $\frac{7}{6}$
B $\frac{5}{2}$

$|4x-2|=8x-12$

$\therefore |x-\frac{1}{2}|=2x-3$

$\therefore (x-\frac{1}{2})=2x-3$ for $x\ge \frac{1}{2}$

and

$-(x-\frac{1}{2})=2x-3$ for $x<\frac{1}{2}$

$⟹x-\frac{1}{2}=-2x+3$ for $x<\frac{1}{2}$

$x-\frac{1}{2}=2x-3$ for $x\ge \frac{1}{2}$

$\therefore x=\frac{5}{2}$ is a solution

$x-\frac{1}{2}=-2x+3$ for $x<\frac{1}{2}$

$\therefore 3x=\frac{7}{2}$

$\therefore x=\frac{7}{6}$

But $x<\frac{1}{2}.$ So, $x=\frac{7}{6}$ is not a solution

So, the answer is option (A).