SOLVING INEQUALITIES USING MULTIPLICATION AND DIVISION WEDNESDAY OCTOBER

SOLVING INEQUALITIES USING MULTIPLICATION AND DIVISION WEDNESDAY OCTOBER 29

WARM UP Solve for x: 1. x – 6 ≥ 3 2. x – 3. 3 ≥ 2. 6 3. -6 > x – 2 4. -2. 5 > x – 0. 9 5. 8. 6 + x < 14

WARM UP And now… In honor of Halloween… A video of a very talkative porcupine eating tiny pumpkins…

SOLVING INEQUALITIES Remember that yesterday we dealt with inequalities just as if they are equations. You can add or subtract numbers from both sides of an inequality to solve for the variable, just like in an equation.

SOLVING INEQUALITIES It gets a little more weird when you multiply and divide numbers on both sides to solve for a variable. We are going to break this section into two parts: multiplying and dividing by positive numbers, and multiplying and dividing by negative numbers.

POSITIVE NUMBERS For example: 3 x > 21 In this case, we want to divide both sides by a POSITIVE NUMBER to solve for the variable x. And we can do that with no problem: 3 x ÷ 3 > 21 ÷ 3 x>7

POSITIVE NUMBERS Likewise: x/2 < 12 In this case, we want to multiply both sides by a POSITIVE NUMBER to solve for the variable x. And we can do that with no problem: 2(x/2) < 2(12) x < 24

POSITIVE NUMBERS When we are dealing with positive numbers, we can multiply or divide just like with an equation.

POSITIVE NUMBERS You try it: 4 x < 12 2. x/4 < 24 3. 3 x ≤ 15 4. x/6 ≥ 3 1.

POSITIVE NUMBERS When we are dealing with positive numbers, we can multiply or divide just like with an equation. But something weird happens when we multiply or divide by a negative number.

POSITIVE NUMBERS When you multiply or divide an inequality by a number, you have to SWITCH THE SIGN Greater than becomes less than, less than becomes greater than.

POSITIVE NUMBERS For example: -3 x < 21 Since you want to divide both sides by a NEGATIVE NUMBER, you need to remember to switch the signs: -3 x ÷ -3 > 21 ÷ -3 x > -7

POSITIVE NUMBERS And: -x/2 < 12 Since you want to multiply both sides by a NEGATIVE NUMBER, you need to remember to switch the signs: -2(-x/2) > -2(12) x > -24

POSITIVE NUMBERS You try it: -4 x < 12 2. -x/4 < 24 3. -3 x ≤ 15 4. -x/6 ≥ 3 1.

HOMEWORK Do Now: Exit Slip Remember I expect every student to participate! These exit slips are your pass to leaving the class! When Done: Turn in to Mr. Johnson Next: Start on homework, Problems 7 -18, page 181