# How do you solve and write the following in interval notation: abs(3(x+2)-7x)<=6?

Oct 16, 2016

$0 \le x \le 3$

#### Explanation:

∣3x+6-7x∣<=6
∣6-4x∣<=6
$6 - 4 x \le 6$ and $- \left(6 - 4 x\right) \le 6$
$- 4 x \le 0$ and $- 6 + 4 x \le 6$
$4 x \ge 0$ and $4 x \le 12$
$x \ge 0$ and $x \le 3$
the answer is $0 \le x \le 3$
Checking, let $x = 2$
LHS $6 - 4 \cdot 2 = - 2$ and ∣-2∣=2
RHS $= 6$
so $2$ is $\le 6$