 Solve
inequalities that contain more than one
operation
Inequalities that contain more than one
operation require more than one step to solve.
Use inverse operations to undo the operations
in the inequality one at a time.
Step 1: Undo addition or subtraction
Step 2: Undo multiplication and division
Is your variable isolated?
Remember!
Subtracting a number is the same as adding its
opposite.
7 – 2t = 7 + (–2t)
Solving Multi-Step Inequalities
Solve the inequality and graph the solutions.
1. Add/ Subtract
45 + 2b > 61
45 + 2b > 61
–45
–45
2b > 16
2. Multiply/Divide
The solution set is {b:b > 8}.
b>8
0
2
4
6
8 10 12 14 16 18 20
Solving Multi-Step Inequalities
Solve the inequality and graph the solutions.
8 – 3y ≥ 29
8 – 3y ≥ 29
–8
–8
1. Add/Subtract
2. Multiply/Divide
–3y ≥ 21
y ≤ –7
The solution set is {y:y  –7}.
–7
–10 –8 –6 –4 –2
0
2
4
6
8 10
Solve and Graph the inequality
1)  9  2b 13
2)2x  13 9
y
3)  12  8
5
4)  3m  5  17

To solve more complicated inequalities, you
may first need to simplify the expressions on
one or both sides.
Simplifying Before Solving Inequalities
Solve the inequality and graph the solutions.
2 – (–10) > –4t
1. Combine like terms.
12 > –4t
2. Multiply/Divide
–3 < t (or t > –3)
The solution set is {t:t > –3}.
–3
–10 –8 –6 –4 –2
0
2
4
6
8 10
Simplifying Before Solving Inequalities
Solve the inequality and graph the solutions.
–4(2 – x) ≤ 8
1. Distributive Property
−4(2 – x) ≤ 8
−4(2) − 4(−x) ≤ 8
–8 + 4x ≤ 8
+8
+8
4x ≤ 16
2. Add/Subtract
3. Multiply/Divide
x≤4
–10 –8 –6 –4 –2
The solution set is {x:x ≤ 4}.
0
2
4
6
8 10
Now you try…
1. 3x – 7 > 2
x>3
4. x – 4 < 3
5
x < 35
2. 4x + 1  -3
x ≥ -1
3. 2x – 7 ≤ -3
x≤2
5. 15 + x ≥ 6
3
x ≥ -27
Lesson Quiz: Part I
Solve each inequality and graph the solutions.
1. 13 – 2x ≥ 21
x ≤ –4
2. –11 + 2 < 3p
p > –3
3. 23 < –2(3 – t)
t>7
4.
Lesson Quiz: Part II
5. A video store has two movie rental plans. Plan A
includes a $25 membership fee plus $1.25 for each
movie rental. Plan B costs $40 for unlimited movie
rentals. For what number of movie rentals is plan B
less than plan A?
more than 12 movies