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**Bell Ringer Solve c – 2 > 20**

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**solve inequalities using multiplication and division.**

6-6 Solving Inequalities by Multiplying or Dividing Objective The student will be able to: solve inequalities using multiplication and division.

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**The inequality stays the same**

POSITIVE NUMBERS ONLY Multiplication & 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. 8p ≥ -96 < -10 ≥ The inequality stays the same

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

NEGATIVE NUMBERS ONLY Multiplication & 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 -8p ≥ -96 > -10 ≤ < -3 The inequality gets flipped every time you * or / by a negative number

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**To solve for a variable the variable must be positive with no number beside it!! **

x = 10 Solved - x = -5 Not solved 2x = 5 Not solved -3x =6 Not solved

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**1) Solve > 13 k < -52 o -52 -51 -53 Draw “the river”**

Clear the fraction - Multiply both sides by -4 NEW STEP!! When multiplying BOTH sides by a NEGATIVE number, SWITCH the inequality! Simplify Check your answer Graph the solution k < -52 o -52 -51 -53

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**2) When solving < -10 will the inequality switch?**

Yes! No! I still don’t know! Answer Now

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**2) Solve < -10 x < -30 o -30 -29 -31 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 < -30 o -30 -29 -31

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**3) When solving will the inequality switch?**

Yes! No! I still don’t know! Answer Now

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**3) Solve a > -24 o -24 -23 -25 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 > -24 o -24 -23 -25

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**4) Solve -8p ≥ -96 p ≤ 12 -8(12) = -96 ● 12 13 11 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 ● 12 13 11

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

-4 -3 -5 Multiply both sides by -4 Switch inequality sign K < -4 o -4 -3 -5 ● -4 -3 -5 ● -4 -3 -5 Answer Now

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**● ● 5) Solve 7v < -105 o o -15 -14 -16 -15 -14 -16 -15 -14 -16 -15**

Divide both sides by 7 V < -15 o -15 -14 -16 ● -15 -14 -16 ● -15 -14 Answer Now

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HW - > page 291 #6-22 even 6-12 show work (2 pts each) 14-20 show work and graph solution (3pts each)

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