Bell RingerSolve

c – 2 > 20

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6-6 Solving Inequalities by Multiplying or Dividing

ObjectiveThe student will be able to:

solve inequalities using multiplication and division.

POSITIVE NUMBERS ONLYPOSITIVE NUMBERS ONLYMultiplication & Division properties of inequalities

You can multiply or divide the same positive number or positive term on each side of the inequality, the relationship between the two sides does not change.

x

3

3 10 33

x

< -108p ≥ -96

8 96

8 8

p

≥The inequality The inequality stays the samestays the same

NEGATIVE NUMBERS ONLYNEGATIVE NUMBERS ONLYMultiplication & Division properties of inequalities

When multiplying or dividing the same negative number or negative term on each side of the inequality, you must reverse the inequality sign

3x

3 10 33

x

> -10-8p ≥ -96

8 96

8 8

p

≤≤<< -3

The inequality gets flipped The inequality gets flipped every time you * or / by a every time you * or / by a

negative numbernegative number

To solve for a variable the To solve for a variable the variable must be positive with variable must be positive with

no number beside it!! no number beside it!! x = 10 Solved

- x = -5 Not solved

2x = 5 Not solved

-3x =6 Not solved

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 ≥ -961. 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-4 -3-5o-4 -3-5●-4 -3-5

-4 -3-5●

1.

2.

3.

4.

Answer NowAnswer Now

1) Which graph represents the correct answer to > 1k

4

Multiply both sides by -4

Switch inequality signK < -4

o-15 -14-16o-15 -14-16●-15 -14-16

-15 -14-15●

1.

2.

3.

4.

Answer NowAnswer Now

5) Solve 7v < -105

Divide both sides by 7

V < -15

HW - > page 291 #6-22 even

6-12 show work (2 pts each)

14-20 show work and graph solution (3pts each)