Inequality Notation:
3x + 10 < -2
or
13 < 3x + 10
To solve for x, let's solve each inequality separately:
1) 3x + 10 < -2
Subtract 10 from both sides:
3x < -12
Divide both sides by 3:
x < -4
2) 13 < 3x + 10
Subtract 10 from both sides:
3 < 3x
Divide both sides by 3:
1 < x
So, the solution for x is x < -4 OR x > 1.
Now let's graph the solution on the number line:
-∞ -----1----- -4------ ∞
↑ ↑
x > 1 x < -4
The shaded region on the number line represents the solution to the inequality. The region to the left of -4 (excluding -4) and the region to the right of 1 (excluding 1) are both solutions.