Solving Inequalities01

Solving Inequalities

Ch 6 lesson 1

Review

• Solve for m

3.15 9.00m

1 55 33 6

m

3.15 9.00m 3.15 3.15

0 5.85m 5.85m

1 55 33 6

m

70 8

6m

196

m

153

256

Inequalities

• Fill in the correct sign

• -7 +6

• +3 -5

• -12 -15

• -3x -7x

What’s the Deal?

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

Solving Inequalities

• Imagine the < or > signs get replaced by an = sign.

• Then just add, subtract, multiply, or divide by the same number on both sides.

• Two special signs– Greater than or equal to

– Less than or equal to

Back to the first slide

3.15 9.00m

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

3.15 9.00m 3.15 3.15

0 5.85m 5.85m

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

Subtract 3.15 from both sides

The answer shows that any number greater than 5.85 will make a true statement.

10 3.15 9.00 13.15 5.85

Check the work

Since 10 is greater than 5.85. Let’s use it to check our work.

Replacing 10 for m, we find a true statement.

We could have picked any number greater than 5.85. 10 is just easy to use.

Fun with graphing

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

5.85m

Number Line

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

Use of closed circles

Greater than or equal to includes the number and everything higher.

Less than or equal to includes the number and everything of lesser value.

Use a closed circle on the number line.

Use a closed circle on the number line.

Use of open circles

Greater than does NOT include the number just every one right up to it.

Less than does NOT include the number, just everything up to it.

Use a closed circle on the number line.

Use a closed circle on the number line.

>

<

Graph m >5.85• 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

That’s too much work

Let’s find a little easier way to graph the inequality.

Graph m >5.85• Start with the number line• You only need to mark 5.85• Put an open circle on 5.85• Fill in everything to greater than 5.85.

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