Solve for xx and graph the solution on the number line below.
3, x, plus, 10, is less than, minus, 2, or, 13, is less than, 3, x, plus, 10
3x+10<−2or
13<3x+10
Answer
Attempt 1 out of 2
Inequality Notation:
Number Line:
Click and drag to plot lin
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.