Solving Inequalities

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Solving Inequalities
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Objective 3.2 The student will be able to

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

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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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3) Graph the solution set ofp ? 2.

• When you have ?, use an open dot and shade both
  ways!

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

1. gt
2. lt
4. ?

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

2. lt
3. gt
4. ?

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6) Solve x (-14) lt 16

• 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  2r14
- 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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Objective 3.3 The student will be able to
solve inequalities using multiplication and
division.
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1) Which graph represents the correct answer to
gt 1

?
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1) Solve gt 13

1. Draw the river
2. Clear the fraction - Multiply both sides by -4
3. NEW STEP!! When multiplying BOTH sides by a
   NEGATIVE number, SWITCH the inequality!
4. Simplify
5. Check your answer
6. Graph the solution

k lt -52
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2) When solving gt -10will the inequality
switch?

1. Yes!
2. No!
3. I still dont know!

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2) Solve lt -10

• Draw the river
• Clear the fraction - Multiply both sides by 3. Do
  you switch the inequality?
• No - Both sides are being multiplied by a
  positive number
• Simplify
• Check your answer
• Graph the solution

x lt -30
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3) When solving will the inequality switch?

1. Yes!
2. No!
3. I still dont know!

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3) Solve

• Draw the river
• Clear the fraction - Multiply both sides by -4.
  Do you switch the inequality?
• Yes - Both sides are being multiplied by a
  negative number
• Simplify
• Check your answer
• Graph the solution

a gt -24
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Take a quick break!

• Things that make you go.....Hmmm
• Why is abbreviation such a long word?
• Why do they have braille dots on the ATM machines
  in drive-thrus?

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4) Solve -8p -96

1. p 12
2. p -12
3. p 12
4. p -12

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4) Solve -8p -96

• Draw the river
• Divide both sides by -8. Do you switch the
  inequality?
• Yes - Both sides are being divided by a negative
  number
• Simplify
• Check your answer
• Graph the solution

p 12 -8(12) -96
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5) Solve 7v lt -105

?