## Intermediate Algebra (6th Edition)

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