Question

Please solve each of the inequalities below and describe the graph.

1. x – 3 > –9

2. –2x + 1 ≤ –11

3. 10 < –3x + 1

4. 2(x + 5) > 8x – 8

5. –2(x – 3) ≥ 5 – (x + 3)

Answer 1

1. x - 3 > -9
x > -9 + 3
x > - 6
open circle on -6, shading to the right.

2. -2x + 1 <= - 11
-2x <= -11 - 1
-2x <= - 12
x => -12/-2 (change signs when dividing by a negative)
x = > 6
closed circle on 6, shading to the right

3. 10 < -3x + 1
10 - 1 < - 3x
9 < - 3x
9/-3 > x
-3 > x
open circle on -3, shading to the left.

4. 2(x + 5) > 8x - 8
2x + 10 > 8x - 8
2x - 8x > -8 - 10
-6x > - 18
x < -18/-6
x < 3
open circle on 3, shading to the left.

5. -2(x - 3) >= 5 - (x + 3)
-2x + 6 > = 5 -x - 3
-2x + x > = 5 - 3 - 6
-x > = -4
x < = 4
closed circle on 4, shading to the left.

Just remember, if there is an equal sign in the problem, it will always be a closed circle. Also, if it is less then, shading goes to the left. If it is greater then, shading goes to the right.

Answer 2

thanks so very much

Answer 3

no problem....glad I could help :)