1. Solving Two-Step Inequalities
Designed by Skip Tyler, Varina High School

2. Solving an inequality is similar to solving an equation, with one main difference.
If you divide the inequality by a negative number, you switch the direction of the symbol.

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

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

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

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

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

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

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

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