How do you solve and graph abs(10-3x)>=17?

Jun 22, 2018

The solution is $x \in \left(- \infty , - \frac{7}{3}\right] \cup \left[9 , + \infty\right)$

Explanation:

This is an inequality with absolute values

$| 10 - 3 x | \ge 17$

Therefore,

$\left\{\begin{matrix}10 - 3 x \ge 17 \\ - 10 + 3 x \ge 17\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}3 x \le 10 - 17 \\ 3 x \ge 17 + 10\end{matrix}\right.$

$\iff$, $\left\{\begin{matrix}x \le - \frac{7}{3} \\ x \ge 9\end{matrix}\right.$

The solution is

$x \in \left(- \infty , - \frac{7}{3}\right] \cup \left[9 , + \infty\right)$

The graph is

graph{|10-3x|-17 [-25.5, 25.83, -17.22, 8.43]}