Using Addition and Subtraction to Solve 2.9 p. 106

Solving Inequalities

What is the objective?

• We will combine the processes from solving addition and subtraction equations with graphing linear inequalities

• We will solve these inequalities and graph the solutions

• As both these skills are review, the PROCESS and INTEGER RULES should be the focus.

Properties of Inequalities Algebraically….this meansProperties of Inequalities Algebraically….this means

If a ≥ b If a ≤ ba + 3 ≥ b + 3 then a + 3 ≤ b + 3

Suppose a = 5 and b = 3 Then (5 + 3) is greater than (3 + 3) 8 > 3

If a ≥ b If a ≤ ba + 3 ≥ b + 3 then a + 3 ≤ b + 3

Suppose a = 5 and b = 3 Then (5 + 3) is greater than (3 + 3) 8 > 3

Note info starts on the next slide.

Solution ExamplesSolution Examples

For inequalities involving only addition and subtraction, solve as if these were equations.

n + 8 ≥ 19

-8 - 8 n ≥ 11

For inequalities involving only addition and subtraction, solve as if these were equations.

n + 8 ≥ 19

-8 - 8 n ≥ 11

11 1210

If a > b If a < ba + c > b + c a – c < b - c

WAIT!!! Listen to the values! n + 8 ≥ 19

$$ + $8 gives me $19 or more than $19

Inequalities are just another neat way to communicate mathematically.

Here is what this inequality is saying to you…..”You had some money, andsomeone gave you another $8. You now have at least $19.

The “n” represents the range of $$$$$ you started with.

Our solution, n ≥ 11 tells us that we could have started with $11.

This would give us a total of $19. Or we could have started with MORE than $11. This would have made the final amount morethan $19.

11 1210

Watch the Signs!Watch the Signs!

-26 > y + 14 You should see the importance of

-14 -14 leaving the variable on the same side!

-40 > y

You will solve and graph several inequalities.Show all work. Create a graph for each solution.

-26 > y + 14 You should see the importance of

-14 -14 leaving the variable on the same side!

-40 > y

You will solve and graph several inequalities.Show all work. Create a graph for each solution.

-40 -39-41

Practice p. 106Practice p. 106

m + 3 > 6 8 + t < 15 -3 ≤ n + 7

-3 -3m > 3

2 3 4

-8 -8t < 7

6 7 8-11 -10 -9

-7 -7 -10 ≤ n

ApplicationApplication

An airline lets you check up to 65 lb. ofluggage with no extra fee.One suitcase weighs 37 lb. What is themost the second suitcase can weigh?

You are writing an inequality BEFOREyou solve!

1st + 2nd bag can be no more than 65

37 + b ≤ 65

-37 -37 b ≤ 28

The second bag can weigh no more than 28 pounds.

Using Addition to SolveWe will solve first, then we will graph.

Using Addition to SolveWe will solve first, then we will graph.

n - 15 < 3 m - 13 > 29

7 ≥ v - 4 11 ≤ t - 5

+ 15 + 15 n < 18

+ 13 +13 m > 42

+4 +4 11 ≥ v

+ 5 +5 16 ≤ t

17 18 19 41 42 43

10 11 12 15 16 17

What was our objective?

• We combined the processes from solving addition and subtraction equations with graphing linear inequalities

• We solved these inequalities and graphed the solutions

• The PROCESS and INTEGER RULES were the focus.

That’s All Folks!