graph inequalities on a number line.

1
ObjectiveThe student will be able to

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

Designed by Skip Tyler, Varina High School
Modified by Lisa Hoffmann, Troy Buchanan High
School
2
Warm Up

• Pg 332 1-9

3
Warm Up Answers

1. Yes
2. No
3. Yes
4. No
5. No
6. Yes
7. 10
8. 24
9. 9

4
1) Graph the solution set ofx lt 3.

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

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

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

6
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

10
7) Solve y 21 7

• - 21 -21
• y -14
• 30 (-14) 16
• 16 16

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

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9) What is the graph of 7 m?

?
12
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

13
1) Which graph represents the correct answer to
gt 1

Remember to use a test point on each side of 4.
Whichever one works is the direction you shade!
?
14
Rules for Solving Inequalities

• You can add the same number (positive or
  negative) to each side of the inequality
• You can subtract the same number (positive or
  negative) from each side of the inequality
• You can multiply OR divide both sides of an
  inequality by a positive number
• WHEN YOU MULTIPLY OR DIVIDE EACH SIDE OF THE
  INEQUALITY BY A NEGATIVE NUMBER YOU MUST CHANGE
  THE DIRECTION OF THE INEQUALITY SYMBOL!

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1) Solve gt 13
-4 k lt 13 -4 -4

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

3 x lt -10 3 3
x lt -30
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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

-4 -a gt 6 -4 -4
x gt -24
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4) Solve -8p -96

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