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Warm Up
Solve each equation.
1. 2x – 5 = –17
2.
Solve each inequality and graph the solutions.
4.
3. 5 < t + 9
–6
14
t > –4
a ≤ –8
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?
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}.
8 – 3y ≥ 29
8 – 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}.
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
–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
–10 –8 –6 –4 –2 0 2 4 6 8 10
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
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.