Question

1. for each inequality, circle two ways to write the solution set and then circle the correct graph.

inequality: -3 > -9 - 3x, 5 > 5x + 15
solution set (choose 2): x < -2, x > -2, -2 < x, -2 > x
graph (choose 1)

Explanation:

Step1: Solve the inequality -3 > - 9 - 3x

Add 9 to both sides of the inequality:
-3+9 > -9 - 3x+9
6 > - 3x
Divide both sides by - 3. When dividing an inequality by a negative number, the direction of the inequality sign changes. So we have $\frac{6}{-3}<\frac{-3x}{-3}$, which simplifies to - 2 < x.

Step2: Solve the inequality 5 > 5x + 15

Subtract 15 from both sides: 5 - 15>5x+15 - 15
-10 > 5x
Divide both sides by 5: $\frac{-10}{5}>\frac{5x}{5}$, which simplifies to - 2>x.

For - 2 < x, the solution - set can be written as {x|x > - 2} and the graph has an open - circle at x = - 2 and the arrow points to the right.
For - 2>x, the solution - set can be written as {x|x < - 2} and the graph has an open - circle at x = - 2 and the arrow points to the left.

Answer:

For -3 > - 9 - 3x:
Solution set: x > - 2, {x|x > - 2}; Graph: Open - circle at - 2, arrow points right.
For 5 > 5x + 15:
Solution set: x < - 2, {x|x < - 2}; Graph: Open - circle at - 2, arrow points left.