# How do you solve the inequality abs(2x+1)<=6-x and write your answer in interval notation?

Apr 3, 2017

$- 7 \setminus \le q x \setminus \le q \frac{5}{3}$

#### Explanation:

Since $| a | \setminus \le q b \setminus \Leftrightarrow - b \setminus \le q a \setminus \le q b$, the inequality $| 2 x + 1 | \setminus \le q 6 - x$becomes

$- \left(6 - x\right) \setminus \le q 2 x + 1 \setminus \le q 6 - x$

$\setminus \Leftrightarrow x - 6 \setminus \le q 2 x + 1 \setminus \le q 6 - x$

$\setminus \Leftrightarrow x - 7 \setminus \le q 2 x \setminus \le q 5 - x$

Solve the inequality on the left:
$x - 7 \setminus \le q 2 x \setminus \Leftrightarrow - 7 \setminus \le q x$

Solve the inequality on the right:
$2 x \setminus \le q 5 - x \setminus \Leftrightarrow 3 x \setminus \le q 5 \setminus \Leftrightarrow x \setminus \le q \frac{5}{3}$

Combine the two intervals: $- 7 \setminus \le q x \setminus \le q \frac{5}{3}$