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Solve inequalities that contain more than one operation
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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.
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Step 1: Undo addition or subtraction
Step 2: Undo multiplication and division
Is your variable isolated?
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Subtracting a number is the same as adding its opposite.7 – 2t = 7 + (–2t)
Remember!
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Solving Multi-Step Inequalities
Solve the inequality and graph the solutions.
45 + 2b > 61
45 + 2b > 61–45 –45
2b > 16
b > 8
0 2 4 6 8 10 12 14 16 18 20
1. Add/ Subtract
2. Multiply/Divide
The solution set is {b:b > 8}.
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8 – 3y ≥ 298 – 3y ≥ 29
–8 –8
–3y ≥ 21
y ≤ –7
1. Add/Subtract
2. Multiply/Divide
–10 –8 –6 –4 –2 0 2 4 6 8 10
–7
Solving Multi-Step Inequalities
Solve the inequality and graph the solutions.
The solution set is {y:y –7}.
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Solve and Graph the inequality
1) 9 2b 13
2)2x 13 9
3)y
5128
4) 3m 5 17
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To solve more complicated inequalities, you may first need to simplify the expressions on one or both sides.
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Simplifying Before Solving Inequalities
Solve the inequality and graph the solutions.
2 – (–10) > –4t
12 > –4t
–3 < t (or t > –3)
1. Combine like terms.
2. Multiply/Divide
–3
–10 –8 –6 –4 –2 0 2 4 6 8 10
The solution set is {t:t > –3}.
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Simplifying Before Solving InequalitiesSolve the inequality and graph the solutions.
–4(2 – x) ≤ 8
−4(2 – x) ≤ 8
−4(2) − 4(−x) ≤ 8–8 + 4x ≤ 8+8 +8
4x ≤ 16
x ≤ 4
1. Distributive Property
2. Add/Subtract
3. Multiply/Divide
–10 –8 –6 –4 –2 0 2 4 6 8 10
The solution set is {x:x ≤ 4}.
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Now you try…
x > 3
x ≥ -1
x ≤ 2
x < 35
x ≥ -27
1. 3x – 7 > 2 4. x – 4 < 3
5
2. 4x + 1 -3
5. 15 + x ≥ 6
3
3. 2x – 7 ≤ -3
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Lesson Quiz: Part ISolve 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.
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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