Lesson: Solving inequalities by multiplying or dividing by a negative

Do Now: (5 minutes)

1) Solve and graph this inequality:

4x + 3 > 15

2) What is the slope of a line that passes through the points (1, 4) and (3, 5)?

3) Solve this inequality, if possible

3x – 2> 3(x + 3)

Direct Instruction: (20 minutes)

Over the last two days, we learned how to solve and graph inequalities on a number line.  We can do inequalities that require multiple steps.  So far, in equalities have followed the same rule as equations.  Today we are going to learn about a rule for inequalities that we did not have to worry about with equations. 

Multiplying and dividing inequalities by a negative number:

1 ___ 5        -1 ___ -5

7 ___ 3        -7 ___ -3

0 ___ 8         0 ___ -8

-1 ___ 2        1 ___ -2

-4 ___ -6       4 ___ 6

What patterns do you notice?

Discuss: real life analogies.

    rich > poor

    -(rich) ___ -(poor)

    That would be <, becasue -(rich) is poor and -(poor) is rich.

    Do a few more like this. [hot/cold, high/low, old/young]

solve a simple equation x/4 >  20 and graph. Check solutions.

    Then solve x/-4 > 20 and graph. Check solutions.

    Discuss why we have to switch the signs.

    Relate to (a) and (b)

With equations there is only one option for the sign between the expressions.  It’s always an equal sign.  With inequalities, however, there are two options.  It can be greater than sign or a less than sign.  This is where the extra rule for inequalities comes in.

When multiplying or dividing both sides of the inequality by a negative number, flip the sign!

Ex. Solve and graph

-3x > 6

Ex. Solve and graph

4 – 2x < 6

Ex. Solve and graph

-2(x – 1) < -22

Guided Practice: (10 minutes)

Students will solve the following problems on white boards

 p/-2 > 7

-2x + 11 < 25

 -3(2x - 1) > 1 - 8x

-3x < 27

 3 - 2x < -17

Assessment: (10 minutes)

Solving inequalities by multiplying or dividing by a negative work-out