The document provides step-by-step instructions for solving various types of two-step inequalities. It begins by stating the objective of teaching students how to solve two-step inequalities. It then works through examples of solving linear inequalities involving variables like m, a, r, p, and x. The examples demonstrate how to isolate the variable by adding, subtracting, multiplying and dividing both sides of the inequality and then checking the solution. Graphs or number line diagrams are provided to illustrate the solution set for each inequality. Multiple choice questions test the understanding of determining the values of a variable that satisfy a given multi-step inequality.

1. Objective
The student will be able to:
solve two-step inequalities.

2. 1) Solve 5m - 8 > 12
+ 8 + 8
5m > 20
5 5
m > 4
5(4) – 8 = 12
1. Draw “the river”
2. Add 8 to both sides
3. Simplify
4. Divide both sides by 5
5. Simplify
6. Check your answer
7. Graph the solution
o
4 53

3. 2) Solve 12 - 3a > 18
- 12 - 12
-3a > 6
-3 -3
a < -2
12 - 3(-2) = 18
1. Draw “the river”
2. Subtract 12 from both
sides
3. Simplify
4. Divide both sides by -3
5. Simplify
(Switch the inequality!)
6. Check your answer
7. Graph the solution
o
-2 -1-3

4. Which graph shows the solution to
2x - 10 ≥ 4?
1. .
2.
3.
4.
Answer Now

5. 3) Solve 5m - 4 < 2m + 11
-2m -2m
3m - 4 < 11
+ 4 + 4
3m < 15
3 3
m < 5
5(5) – 4 = 2(5) + 11
1. Draw “the river”
2. Subtract 2m from both
sides
3. Simplify
4. Add 4 to both sides
5. Simplify
6. Divide both sides by 3
7. Simplify
8. Check your answer
9. Graph the solution
o
5 64

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

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

8. 5) Solve 26p - 20 > 14p + 64
-14p -14p
12p – 20 > 64
+ 20 + 20
12p > 84
12 12
p > 7
26(7) – 20 = 14(7) + 64
1. Draw “the river”
2. Subtract 14p from both
sides
3. Simplify
4. Add 20 to both sides
5. Simplify
6. Divide both sides by 12
7. Simplify
8. Check your answer
9. Graph the solution
o
7 86

9. What are the values of x if
3(x + 4) - 5(x - 1) < 5?
Answer Now
1. x < -6
2. x > -6
3. x < 6
4. x > 6

10. What are the values of x if
3(x + 4) - 5(x - 1) < 5?
Answer Now
1. x < -6
2. x > -6
3. x < 6
4. x > 6