# How do you solve |14n+3|>=18?

Oct 31, 2016

Solution: $- \frac{3}{2} \ge n \ge \frac{15}{14}$. In interval notation expressed as $\left(- \infty , - \frac{3}{2}\right] \cup \left[\frac{15}{14} , \infty\right)$
1) $| 14 n + 3 | \ge 18 \mathmr{and} 14 n + 3 \ge 18 \mathmr{and} 14 n \ge 15 \mathmr{and} n \ge \frac{15}{14}$ OR
2)$| 14 n + 3 | \ge 18 \mathmr{and} 14 n + 3 \le - 18 \mathmr{and} 14 n \le - 21 \mathmr{and} n \le - \frac{21}{14} \mathmr{and} n \le - \frac{3}{2}$
Solution:$- \frac{3}{2} \ge n \ge \frac{15}{14}$ In interval notation expressed as $\left(- \infty , - \frac{3}{2}\right] \cup \left[\frac{15}{14} , \infty\right)$[Ans]