SOLVING INEQUALITIES USING MULTIPLICATION AND DIVISION THURSDAY OCTOBER

SOLVING INEQUALITIES USING MULTIPLICATION AND DIVISION THURSDAY OCTOBER 30

WARM UP Solve for x: 1. 3 x ≥ 27 2. x/2 ≥ 4. 2 3. -6 > 2 x 4. -2. 5 > 2. 5 x 5. x/4 < 2

WARM UP And now… In honor of Halloween… Possibly the greatest use ever of a toy drone and a Halloween costume…

GRADES I have not graded the work that was turned in yesterday, and the grades I have in my grade book have not been entered into the computer yet. So, NO, I don’t know what your grade is today. It will be online on Friday.

TESTING Due to overwhelming demand for retakes of tests and constant comments of “Can I take the test Thursday? ” I will have a test retake sign-up sheet posted starting Monday. I don’t need to hear about you wanting to take a test – SIGN UP!

SOLVING INEQUALITIES So yesterday we talked about solving inequalities using multiplication and division, and I told you that if you multiply or divide by a negative number you need to change the sign. MANY students scratched their head and said, “Why? ”

SOLVING INEQUALITIES So lets look at all of the different ways we can talk about inequalities, and see why this makes sense.

SOLVING INEQUALITIES 4>2 We can all agree that four is indeed greater than two. So what happens when we add 5 to both sides? 9>7 Is nine greater than seven? Yes!

SOLVING INEQUALITIES 4>2 What happens when we subtract six from both sides? -2 > -4 Is negative two greater than negative four? Yes!

SOLVING INEQUALITIES 4>2 What happens when we multiply both sides by five? 20 > 10 Is twenty greater than ten? Yes!

SOLVING INEQUALITIES 4>2 And what happens when we divide both sides by two? 2>1 Is two greater than one? Yes!

SOLVING INEQUALITIES So we see that if we multiply or divide both sides of any inequality by an positive number, and if we add or subtract any number, the inequality is true.

SOLVING INEQUALITIES 4>2 And what happens when we multiply both sides by negative three? -12 > -6 Is negative twelve greater than negative six? No!

SOLVING INEQUALITIES Negative twelve is LESS THAN negative six, so we need to change the sign from greater than to less than when we multiply by a negative number -12 < -6

SOLVING INEQUALITIES 4>2 And what happens when we divide both sides by negative one? -4 > -2 Is negative four greater than negative two? No!

SOLVING INEQUALITIES Negative four is LESS THAN negative two, so we need to change the sign from greater than to less than when we divide by a negative number -4 < -2

SOLVING INEQUALITIES So remember that you can add or subtract any number from both sides of an inequality and nothing changes. And you can multiply or divide both sides of an equation by a positive number, and nothing changes.

SOLVING INEQUALITIES But if you multiply/divide both sides by a negative number, then the inequality sign changes direction. > becomes < < becomes > ≥ becomes ≤ ≤ becomes ≥

YOU TRY: Solve for x: 1. -3 x ≥ 27 2. -x/2 ≥ 4. 2 3. -6 > -2 x 4. -2. 5 > -2. 5 x 5. -x/4 < 2

A REAL FIND GAME Each member of the class will team up with a partner. Each team will get a set of sheets with different values on them. One will be labeled INEQUALITIES and the other will be labeled ANSWERS.

A REAL FIND GAME The one holding the sheet labeled INEQUALITIES will read aloud an inequality from the list. The other student holding the sheet label ANSWERS will try to find the inequality that is equal to the one read aloud by his or her partner. Once found, write the matching inequalities on each sheet.

A REAL FIND GAME Once you have found a matching pair, switch sheets with your partner as they read aloud a new inequality to find. Keep going on the sheets until all of the inequalities have been found. Participation is not optional! I should see ALL students teamed up and working! Write your names at the top.

HOMEWORK Do Now: A Real Find Game 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