how do you solve |3x+7| is greater than or equal to 26

Question

anonymous · Answer

you are taking the absolute value of 3x+7| >= 26 so you write out the inequality and solve

anonymous · Answer

When you see I I, it means absolute value, or the distance from 0. This means the number isn't changing, but if it's negative, it will be a positive number instead. Absolute value always means a positive number. So, I3x+7I is greater or equal to (greater than sign with line under it) to 26. Whatever x is, you'd plug it in.

kirbykirby · Answer

$$|x|=\begin{cases} x &,\text{if }x\ge 0\ -x&,\text{if }x<0\end{cases} $$
Then:
$$|3x+7|=\begin{cases} 3x+7 &,\text{if }3x+7\ge 0\ -(3x+7)&,\text{if }3x+7<0\end{cases} $$

So you have two cases to solve for:
$(3x+7) \ge 26$
and
$-(3x+7)\ge 26$