1. Learning Target: The student will be able to
Solve and Graph two-step inequalities.

2. Inequalities and their graphs
Inequality - a mathematical sentence that contains <,>,<, > or not equal.
reads as greater than
reads as less than
< reads as less than or equal to
> reads as greater than or equal to
≠ not equal to

3. Inequalities and their graphs
When graphing inequalities use
Open circle used for <, >
Shaded circle used for >, <

4. Inequalities and their graphs-answers
When graphing inequalities use
Open circle used for <, >
Shaded circle used for >, <

5. Inequalities and their graphs

6. Solving One-Step Inequalities
Examples:
x - 15 < M - 13 > 29
3. V - 4 < T - 5 > 11
< y X - 9 > -11

7. Solving One-Step Inequalities - ans
Examples:
x - 15 < M - 13 > 29
x < m > 42
3. V - 4 < T - 5 > 11
v < T > 16
< y - 14 y > X - 9 > -11 x > -2

8. Solve Two-Step Inequalities
Solve the same way as solving two-step equations.
When dividing or multiplying by a negative number you must reverse (flip) the inequality sign

9. 1) Solve 5m - 8 > 12 + 8 + 8 5m > 20 5 5 m > 4 5(5) – 8 = 12
Add 8 to both sides
Divide both sides by 5
Check your answer
Graph the solution
5m > 20
m > 4
5(5) – 8 = 12 o 4 5 3

10. 2) Solve 12 - 3a > 18 - 12 - 12 -3a > 6 -3 -3 a < -2
-3a > 6
a < -2
12 - 3(-3) = 18
Subtract 12 from both sides
Divide both sides by -3
(Switch the inequality!)
Check your answer
Graph the solution o -2 -1 -3

11. Which graph shows the solution to 2x - 10 ≥ 4?.
Answer Now

12. 3) Solve 5m - 4 < 2m + 11 o -2m -2m 3m - 4 < 11 + 4 + 4
3m < 15
m < 5
5(4) – 4 = 2(4) + 11
Subtract 2m from both sides
Add 4 to both sides
Divide both sides by 3
Check your answer
Graph the solution o 5 6 4

13. 4) Solve 2r - 18 ≤ 5r + 3 ● -2r -2r -18 ≤ 3r + 3 - 3 - 3 -21 ≤ 3r 3 3
Subtract 2r from both sides
Subtract 3 from both sides
Divide both sides by 3
Check your answer
Graph the solution
-2r r
-18 ≤ 3r + 3
-21 ≤ 3r
-7 ≤ r or r ≥ -7
2(-7) – 18 = 5(-7) + 3 ● -7 -6 -8

14. 6) Solve -2x + 6 ≥ 3x - 4
x ≥ -2
x ≤ -2
x ≥ 2
x ≤ 2
Answer Now

15. 5) Solve 26p - 20 > 14p + 64 o -14p -14p 12p – 20 > 64 + 20 + 20
12p > 84
p > 7
26(8) – 20 = 14(8) + 64
Subtract 14p from both sides
Add 20 to both sides
Divide both sides by 12
Check your answer
Graph the solution o 7 8 6

16. What are the values of x if 3(x + 4) - 5(x - 1) < 5?
Answer Now