rnotes - willjarms.enschool.org
TRANSCRIPT
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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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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 ≥ 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 d –7}.
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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
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Name: _____________________________
Solving Two-Step Inequalities – (Lesson 4.4)
x You can solve two-step _________________________ in the same way you solve two-step equations.
Solving Two-Step Inequalities:
Solve.
5x – 4 ≥ 11 3�b + 4 < 13 19 ≤ 4 – 3d
6y – 7 > 5 9 < 4�w + 8 -17 ≤ 3y – 4
Graphing an Inequality:
Solve and Graph.
-7(x + 3) ≤ 28 -3 ≤ 0.5( 8 + y)
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Real-Life Application:
A contestant in a weight-loss competition wants to lose an average of at least 8 pounds per month during a 5-month period. How many pounds must the constant lose in the fifth month to meet the goal?
Progress Report
Month Pound Lost
1 12 2 9 3 5 4 8
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Name : Score :
Printable Math Worksheets @ www.mathworksheets4kids.com
Solve each inequality.
2x + 5 > 131) 2) 5x – 7 ≥ 83)
4) 9x – 3 > 65) 11 + 3x ≤ 176)
8) 9)4x – 12 ≥ 87)
10) 7x – 3 > 1811) 12)
3x + 7 < 9
3x + 1 ≥ 7
x – 43
≤ 5
x4
+1 > 10
x – 64
≤ 2
x2
+ 4 < 7
Solving Two-Step Inequalities ES1
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Name : Score :
Printable Math Worksheets @ www.mathworksheets4kids.com
Solve each inequality.
2x + 5 > 131) 2) 5x – 7 ≥ 83)
4) 9x – 3 > 65) 11 + 3x ≤ 176)
8) 9)4x – 12 ≥ 87)
10) 7x – 3 > 1811) 12)
3x + 7 < 9
3x + 1 ≥ 7
x – 43
≤ 5
x > 4
x ≥ 5
x ≤ 14
x < 6
x ≥ 3
x > 36
x ≥ 2
x ≤ 2
x4
+1 > 10
x > 1
x > 3
x ≤ 19
x < 23
x – 64
≤ 2
x2
+ 4 < 7
Solving Two-Step Inequalities
Answer key
ES1
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Name : Score :
Printable Math Worksheets @ www.mathworksheets4kids.com
Solve each inequality and graph the solution.
3) 7x – 19 < 16
2) 4x + 5 ≤ 13
8) 2x + 5 ≥ 19
2 4 60-2-4 8
5) 9 + 3x > 12 6) 3x – 4 ≤ 5
4)
7)
0 10 20-10-20-30 30 7 14 210-7-14 28
3 5 7-1-3 9
1)
x – 45
≥ 2
x8
+ 1 < 3
-1 0 1 2 3 4-2-3-4-5-6 5 6
5 15-15-25 25-5
0 2 4 61 8-2 1 3 5 7-1-3
0 8 16-8-16-24 24 -7 0 7 14 21 28-14-21-28-35-42 35 42
x2
+ 3 > 9
-2 0 2 4 6 8-4 10 12 14 16 18 20
Solving & Graphing Inequalities ES1
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Name : Score :
Printable Math Worksheets @ www.mathworksheets4kids.com
Solve each inequality and graph the solution.
3) 7x – 19 < 16
x > 12 x ≤ 2
x < 5
2) 4x + 5 ≤ 13
x ≥ 14
x > 1
8) 2x + 5 ≥ 19
x ≤ 3
2 4 60-2-4 8
5) 9 + 3x > 12
x < 16
6) 3x – 4 ≤ 5
x ≥ 7
4)
7)
0 10 20-10-20-30 30 7 14 210-7-14 28
3 5 7-1-3 9
1)
x – 45
≥ 2
x8
+ 1 < 3
-1 0 1 2 3 4-2-3-4-5-6 5 6
5 15-15-25 25-5
0 2 4 61 8-2 1 3 5 7-1-3
0 8 16-8-16-24 24 -7 0 7 14 21 28-14-21-28-35-42 35 42
x2
+ 3 > 9
-2 0 2 4 6 8-4 10 12 14 16 18 20
Solving & Graphing Inequalities
Answer key
ES1
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Name :Teacher : Date :
Score :
Math-Aids.Com
Solve and Graph the InequalitiesSolve and Graph the Inequalities
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Name :Teacher : Date :
Score :
Math-Aids.Com
Solve and Graph the InequalitiesSolve and Graph the Inequalities
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