Answer
$(-∞,-\frac{3}{7}]U[1,∞)$
Work Step by Step
We are given that $|7x-2|\geq5$, so we know that $7x-2\geq5$ or $7x-2\leq-5$. We can solve these equations to find solutions for x.
For $7x-2\geq5$, add 2 to both sides.
$7x\geq7$
Divide both sides by 7.
$x\geq1$
For $7x-2\leq-5$, add 2 to both sides.
$7x\leq-3$
Divide both sides by 7.
$x\leq-\frac{3}{7}$