Bell Ringer 9/26/14

Test Questions

ObjectiveThe student will be able to:

1. graph inequalities on a number line.

2. solve inequalities using addition and subtraction.

1) Graph the solution set ofx < 3.

When you have < or >, 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.>

2.<

3.≥

4.≠Answer NowAnswer Now

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

1.≤

2.<

3.>

4.≠Answer NowAnswer Now

6) Solve x + (-14) < 16

x - 14 < 16 + 14 +

14 x < 30

30 + (-14) = 1616 = 16

Solve this problem like an equation

1. Draw “the river”2. Eliminate double

signs3. Add 14 to both sides4. Simplify5. Check your answer6. Graph the solution

o30 3129

7) Solve y + 21 ≥ 7

- 21 -21

y ≥ -14

(-14) + 21 = 7

7 = 7

1. Draw the “river”2. Subtract 21 from

both sides3. Simplify4. Check your answer5. Graph the solution

-14 -13-15●

8) Solve 8y + 3 > 9y - 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

o17 1816

- 8y - 8y

3 > y - 14

+ 14 + 14

17 > y

y < 178(17) + 3 = 9(17) - 14

9) What is the graph of 7 ≤ m?

1.

2.

3.

4.

o7 86o7 86●7 86

7 86●

Answer NowAnswer Now

10) Solve 3r - 17 ≥ 2r + 14

●31 3230

- 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

11) Solve -2x + 6 ≥ 3x - 4

1. x ≥ -2

2. x ≤ -2

3. x ≥ 2

4. x ≤ 2

Answer NowAnswer Now

12) Joanna’s 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

Answer NowAnswer Now

ObjectiveThe student will be able to:

solve inequalities using multiplication and division.

o-4 -3-5o-4 -3-5●-4 -3-5

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1) Which graph represents the correct answer to > 1

1.

2.

3.

4.

Answer NowAnswer Now

k

4

1) Solve > 13k

4

o-52 -51-53

k < -52

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

4 13 -44

k

152

34

2) When solving > -10will the inequality switch?

1.Yes!

2.No!

3. I still don’t know!

x

3

Answer NowAnswer Now

2) Solve < -10 x

3

o-30 -29-31

x < -30

1. Draw “the river”

2. Clear the fraction - Multiply both sides by 3. Do you switch the inequality?

No - Both sides are being multiplied by a positive number

3. Simplify

4. Check your answer

5. Graph the solution

3 10 33

x

030

13

3) When solvingwill the inequality switch?

1.Yes!

2.No!

3. I still don’t know!

a4

6

Answer NowAnswer Now

3) Solve a4

6

o-24 -23-25

a > -24

1. Draw “the river”

2. Clear the fraction - Multiply both sides by -4. Do you switch the inequality?

Yes - Both sides are being multiplied by a negative number

3. Simplify

4. Check your answer

5. Graph the solution

-4 6 -44

a

24( )6

4

4) Solve -8p ≥ -96

1.p ≥ 12

2.p ≥ -12

3.p ≤ 12

4.p ≤ -12Answer NowAnswer Now

4) Solve -8p ≥ -96

1. Draw “the river”

2. Divide both sides by -8. Do you switch the inequality?

Yes - Both sides are being divided by a negative number

3. Simplify

4. Check your answer

5. Graph the solution

8 96

8 8

p

p ≤ 12

-8(12) = -96

●12 1311

o-15 -14-16o-15 -14-16●-15 -14-16

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5) Solve 7v < -105

1.

2.

3.

4.

Answer NowAnswer Now

ObjectiveThe student will be able to:

solve two-step inequalities.

1) Solve 5m - 8 > 12

+ 8 + 8

5m > 20

5 5

m > 4

5(4) – 8 = 12

1. Draw “the river” 2. Add 8 to both sides3. Simplify4. Divide both sides by 55. Simplify6. Check your answer7. Graph the solution

o4 53

2) Solve 12 - 3a > 18

- 12 - 12

-3a > 6

-3 -3

a < -2

12 - 3(-2) = 18

1. Draw “the river” 2. Subtract 12 from both

sides3. Simplify4. Divide both sides by -3 5. Simplify

(Switch the inequality!)6. Check your answer7. Graph the solution

o-2 -1-3

Which graph shows the solution to 2x - 10 ≥ 4?

1. .

2.

3.

4.

Answer NowAnswer Now

3) Solve 5m - 4 < 2m + 11

-2m -2m

3m - 4 < 11

+ 4 + 4

3m < 15

3 3

m < 5

5(5) – 4 = 2(5) + 11

1. Draw “the river” 2. Subtract 2m from both

sides3. Simplify4. Add 4 to both sides5. Simplify6. Divide both sides by 3 7. Simplify8. Check your answer9. Graph the solution

o5 64

4) Solve 2r - 18 ≤ 5r + 3-2r -2r

-18 ≤ 3r + 3

- 3 - 3

-21 ≤ 3r

3 3

-7 ≤ r or r ≥ -7

2(-7) – 18 = 5(-7) + 3

1. Draw “the river” 2. Subtract 2r from both sides3. Simplify4. Subtract 3 from both sides5. Simplify6. Divide both sides by 3 7. Simplify8. Check your answer9. Graph the solution

●-7 -6-8

6) Solve -2x + 6 ≥ 3x - 4

1. x ≥ -2

2. x ≤ -2

3. x ≥ 2

4. x ≤ 2

Answer NowAnswer Now

5) Solve 26p - 20 > 14p + 64 -14p -14p

12p – 20 > 64

+ 20 + 20

12p > 84

12 12

p > 7

26(7) – 20 = 14(7) + 64

1. Draw “the river” 2. Subtract 14p from both

sides3. Simplify4. Add 20 to both sides5. Simplify6. Divide both sides by 12 7. Simplify8. Check your answer9. Graph the solution

o7 86

What are the values of x if 3(x + 4) - 5(x - 1) < 5?

1. x < -6

2. x > -6

3. x < 6

4. x > 6

Answer NowAnswer Now

ObjectivesThe student will be able to:

1. solve compound inequalities.

2. graph the solution sets of compound inequalities.

1) Graph x < 4 and x ≥ 2

3 42●

a) Graph x < 4

b) Graph x ≥ 23 42

o

c) Combine the graphs

●

3 42o

d) Where do they intersect?●

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2) Graph x < 2 or x ≥ 4

3 42●

a) Graph x < 2

b) Graph x ≥ 43 42

o

c) Combine the graphs

3 42o

3 42●

3) Which inequalities describe the following graph?

1. y > -3 or y < -1

2. y > -3 and y < -1

3. y ≤ -3 or y ≥ -1

4. y ≥ -3 and y ≤ -1

-2 -1-3oo

Answer NowAnswer Now

4) Graph the compound inequality 6 < m < 8

When written this way, it is the same thing as

6 < m AND m < 8

It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however,

it is easier to graph everything

between 6 and 8!

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5) Which is equivalent to-3 < y < 5?

1. y > -3 or y < 5

2. y > -3 and y < 5

3. y < -3 or y > 5

4. y < -3 and y > 5

Answer NowAnswer Now

6) Which is equivalent to x > -5 and x ≤ 1?

1. -5 < x ≤ 1

2. -5 > x ≥ 1

3. -5 > x ≤ 1

4. -5 < x ≥ 1

Answer NowAnswer Now

7) 2x < -6 and 3x ≥ 121. Solve each inequality for x

2. Graph each inequality

3. Combine the graphs

4. Where do they intersect?

5. They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!!

2 6

2 2 3

x

x

3x 12

3 3 x 4

-3 0-6o-3 0-6o

4 71o●4 71o●

8) Graph 3 < 2m – 1 < 9

Remember, when written like this, it is an AND problem!

3 < 2m – 1 AND 2m – 1 < 9Solve each inequality.

Graph the intersection of 2 < m and m < 5.

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9) Graph x < 2 or x ≥ 4

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10) Graph x ≥ -1 or x ≤ 3

The whole line is shaded!!

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