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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. Inequalities:. Solve Inequalities by Adding or Subtracting.

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Section 5.4 Solving Inequalities

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  1. 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 2009. 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 45. 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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