6 2solving Inequalities

Solving Multi-stepInequalities

Ch 6 lesson 2

Review

• Solve for m

3 900x

19

3x

3 900x

3 900

3 3x

1 300x

300x

19

3x

3 19 3

1 3x

1 27x

27x

What’s the Deal?

In today’s lesson we will solve multi-step inequalities and graph them using a number line.

These will be similar to the multi-step equations that we worked through n Unit Three.

Back to Unit Three, But with an Inequality

9x

This should look similar to your first equation. The greater than sign replaces the equal sign.

1 9x

9x

Work the algebra problem just like you would with the = sign

9x Divide negative 1 from

both sides

The answer shows that any number greater than 9 will make a true statement.

1 9

1 1

x

Fun with graphing

We can use a number line to show all the numbers that work for m.

9x

-6 -4 -2 0 +2 +4 +6

Graph x >9• Start with the number line

• Put an open circle on 5.85

• Fill in everything to greater than 5.85.

-6 -4 -2 0 +2 +4 +6

OR Graph x >9• Start with the number line• You only need to mark 9• Put an open circle on 9• Fill in everything to greater than 9.

9

10x

Work the multi-step algebra problem just like you would with the = sign, then graph.

3 (2 6 ) 28x x

3 2 6 28x x

2 3 28x 2 2

1 10x

3 30

3 3x

-10

10x

Another twist to algebra

1 10x

3 30

3 3x

-10

Whenever you multiply or divide BY A NEGATIVE NUMBER you must

flip the inequality.

10x

Let’s check our work

10x-10

Pick an number from the graphed answer set to see if this works.

+10

3(10) (2 6(10) 28

30 (62) 28

32 28

Try one. Solve for x and graph the inequality.

c + 7 < -11

Solutionc + 7 – 7 < -11 – 7

c + 0 < -18

-18

Greater than or equal to has a closed circle.

Graph 3x

-3

Check your work.Could 10 be a solution for x?

3x-3

10 3Ten is part of the graphed solution

+10

Summary

• Solving inequalities is similar to solving other algebraic equations.

• Use open circles for greater than (>) or less than (<).

• Use closed circles to show less-than-or equal-to and greater-than-or-equal-to.

Assignment: pg. 280 :15 – 29; 36-37; 43, 45