1. Section 5.4 Solving Inequalities
Name __________________
Section 5.4 Solving Inequalities
Objectives:
Solve inequalities by using the Addition and Subtraction properties of Inequality
Solve inequalities by multiplying or dividing by a positive or negative number

2. Inequalities:

3. Solve Inequalities by Adding or Subtracting
When you add or subtract the same number from each side of an inequality, the inequality remains true
Examples:
1. y + 10 < 3
2. x + 7 > 10

4. Graphing

5. Solve Inequalities by Multiplying or Dividing by a Positive Number
Some inequalities like 4x > 8 are solved by multiplication or division.
You can multiply or divide each side of an inequality by a positive number and the inequality is still true.

6. Real-World Example
5. Macy is making each of her 7 friends a bracelet. She does not want to spend more than $40 on the bracelets. Write an inequality and find the maximum cost for each bracelet.

7. Multiply or Divide an Inequality by a Negative Number
What happens when each side of an inequality is multiplied or divided by a negative number?
Ex. Graph 2 and 4 on a number line
Now, multiply each number by -1

8. Multiply or Divide an Inequality by a Negative Number
Notice that the numbers being compared switched positions as a result of being multiplied by a negative number.
In other words, their order reversed.

9. Examples

10. Word Problems
3. The 2008 attendance at the Ohio State Fair was at least 16,700 less than the attendance in If the attendance in 2008 was 809,300, write and solve an inequality to find the 209 attendance.

11. Word Problems
4. Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how man hours she needs to work to earn at least $120.

12. H.O.T. Problems
1. Twenty more than half a number is at least Find the least number that meets this condition.
2. Is the following statement true or false? If false, provide a counterexample.
For all values of x, two times x is greater than x

13. Essential Question
How is solving an inequality similar to solving an equation?
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