Graphing, Writing and Solving Inequalities

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Graphing, Writing and Solving Inequalities
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ObjectiveThe student will be able to

1. graph inequalities on a number line.
2. solve inequalities using addition and subtraction.

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Graphing Inequalities
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1) Graph the solution set ofx lt 3.

• When you have lt or gt, use an open dot!

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2) Graph the solution set ofy -5/4.

• When you have or , use a closed dot!
• Converting -5/4 to a decimal -1.25

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4) Which inequality would have a closed dot on
the number line?

1. gt
2. lt

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5) Which inequality does NOT use an open dot on
the number line?

2. lt
3. gt

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Writing Inequalities from a Graph
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6) Solve x (-14) lt 16
Solving Inequalities with Addition and Subtraction

• x - 14 lt 16
• 14 14
• x lt 30
• 30 (-14) 16
• 16 16

• Solve this problem like an equation
• Draw the river
• Eliminate double signs
• Add 14 to both sides
• Simplify
• Check your answer
• Graph the solution

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7) Solve y 21 7

• - 21 -21
• y -14
• (-14) 21 7
• 7 7

1. Draw the river
2. Subtract 21 from both sides
3. Simplify
4. Check your answer
5. Graph the solution

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8) Solve 8y 3 gt 9y - 14
- 8y - 8y 3 gt y - 14
14 14 17 gt y
y lt 17 8(17) 3 9(17) - 14

1. Draw the river
2. Subtract 8y from both sides
3. Simplify
4. Add 14 to both sides
5. Simplify
6. Rewrite inequality with the variable first
7. Check your answer
8. Graph the solution

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9) What is the graph of 7 m?

?
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10) Solve 3r - 17  2r 14
- 2r - 2r r 17 14
17 17 r 31 3(31) -
17 2(31) 14

1. Draw the river
2. Subtract 2r from both sides
3. Simplify
4. Add 17 to both sides
5. Simplify
6. Check your answer
7. Graph the solution

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11) Solve -2x 6 3x - 4

1. x -2
2. x -2
3. x 2
4. x 2

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12) Joannas tests were 87, 93, 88 and 94. What
must her 5th grade be to get a total of at least
459?

1. 96
2. 97
3. 98
4. 100

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Summation of Adding and Subtracting Inequalities