# How do you solve the inequality abs(7x+2)>10 and write your answer in interval notation?

Solution: $x > \frac{8}{7} \mathmr{and} x < - \frac{12}{7}$. In interval notation : $\left(- \infty , - \frac{12}{7} ,\right) \cup \left(\frac{8}{7} , \infty\right)$
$| 7 x + 2 | > 10 \mathmr{and} 7 x + 2 > 10 \mathmr{and} 7 x > 8 \mathmr{and} x > \frac{8}{7} \mathmr{and} x > 1 \frac{1}{7}$ OR
$| 7 x + 2 | > 10 \mathmr{and} 7 x + 2 < - 10 \mathmr{and} 7 x < - 12 \mathmr{and} x < - \frac{12}{7} \mathmr{and} x < - 1 \frac{5}{7}$
Solution: $x > \frac{8}{7} \mathmr{and} x < - \frac{12}{7}$. In interval notation : $\left(- \infty , - \frac{12}{7} ,\right) \cup \left(\frac{8}{7} , \infty\right)$ [ANS]