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Assignment # _____ Solving Two-Step Inequalities
and REVIEW
Standard: AF 4.1 Solve two-step inequalities
AF 4.1 Solve two-step equations
Name _________________________
Pre-Algebra, Period ______
Date __________________________
Solve a two-step inequality
Example:
4y +10 < 18
4y + 10 – 10 < 18 – 10
4y < 8
4y 8

4 4
y<2

Solve a two-step inequality
Example:
–3x + 10 < 31
–3x + 10 – 10 < 31 – 10
original inequality
subtract 10 from both sides
simplify
divide each side by 4
simplify
original inequality
subtract 10 from both sides
–3x < 21
simplify
3x 21

3
3
divide each side by –3 and reverse the inequality symbol
x > –7
simplify

Remember:
 goes with < and >
 goes with < and >
Solve the inequality. Then graph the solution.
1. 4y + 6 < 38
2. –2p + 4 > 14
3. 3n – 6 > 18
4. –2x + 1 < 15
Solve the inequality or equation.
5. 7a + 5 > 40
6.
y
 8  11
6
7. 6x + 32 = 50

8. 4x – 6 = 42
11.
x
5  4
8
9. 9x – 12 = 24
10. –7x – 6 = 8
12. –3x + 5 > –16
13. –5x + 14 = –21

14. What is the solution set to the inequality 7z + 5 > 47?
A {z : z < 5}
B {z: z > 6}
C {z : z < 6}
14. ______
D {z : z > 24}
15. What value of x satisfies the equation 3x + 6 = 24?
A 10.0
B 5.0
C 6.0
15. ______
D 7.5
16. A group order 6 meals that cost x dollars each and leaves a $14 tip.
The group spends a total of $86. If the equation shows the relationship,
how much did each person pay before the tip?
6x + 16 = 88
A $72
B $104
C $16
16. ______
D $12