Answer
$x=-\frac{1}{7}$
Work Step by Step
We are given that $|7x-2|=|7x+4|$. Therefore, $7x-2=7x+4$ and $7x-2=-(7x+4)$. We can solve both equations to find solutions.
For $7x-2=7x+4$, subtract 7x from both sides.
$-2=4$
This is not true, so this equation has no solution.
For $7x-2=-(7x+4)$, use the distributive property to simplify the right side.
$7x-2=-7x-4$
Add 7x to both sides.
$14x-2=-4$
Add 2 to both sides.
$14x=-2$
Divide both sides by 14.
$x=-\frac{1}{7}$