Presentation is loading. Please wait.

Presentation is loading. Please wait.

2-5 Solving Inequalities Containing Integers Course 3 Lesson Presentation Lesson Presentation.

Similar presentations


Presentation on theme: "2-5 Solving Inequalities Containing Integers Course 3 Lesson Presentation Lesson Presentation."— Presentation transcript:

1 2-5 Solving Inequalities Containing Integers Course 3 Lesson Presentation Lesson Presentation

2 Learn to solve inequalities with integers. Course Solving Inequalities Containing Integers

3 Course Solving Inequalities Containing Integers When you pour salt on ice, the ice begins to melt. If enough salt is added, the resulting saltwater will have a freezing point of –21°C, which is much less than waters freezing point of 0°C. At its freezing point, a substance begins to freeze. To stay frozen, the substance must maintain a temperature that is less than or equal to its freezing point. Adding rock salt to the ice lowers the freezing point and helps to freeze the ice cream mixture.

4 If you add salt to the ice that is at a temperature of –4°C, what must the temperature change be to keep the ice from melting? Course Solving Inequalities Containing Integers This problem can be expressed as the following inequality: –4 + t –21 When you add 4 to both sides and solve, you find that if t –21, the ice will remain frozen.

5 Course Solving Inequalities Containing Integers The graph of an inequality shows all of the numbers that satisfy the inequality. When graphing inequalities on a number line, use solid circles ( ) for and and open circles ( ) for > and <. Remember!

6 Course Solving Inequalities Containing Integers k > –5 A. k +3 > –2 Subtract 3 from both sides. –3 k +3 > –2 Solve and graph. Additional Example 1A: Adding and Subtracting to Solve Inequalities –5 0

7 Course Solving Inequalities Containing Integers B. r – 9 12 r 21 Add 9 to both sides. r – r – Additional Example 1B: Adding and Subtracting to Solve Inequalities Continued Solve and graph.

8 15-Feb-14 Solving inequalities is almost identical to solving equations : Solving Inequalities Example 1 x is any value less than 4 Even Better News !

9 15-Feb-14 Solving inequalities is almost identical to solving equations : Solving Inequalities Example 2 x is any value greater than or equal to 5

10 –5 1 Course Solving Inequalities Containing Integers 5 is greater than –1. Sometimes you must multiply or divide to isolate the variable. Multiplying or dividing both sides of an inequality by a negative number gives a surprising result. 5 > –1 Multiply both sides by –1. –1 5 –1 (–1) > or < ? You know –5 is less than 1, so you should use <. –5 < 1 –7 –6 –5 –4 –3 –2 – –5 < 1 5 > –1

11 Course Solving Inequalities Containing Integers 3 > 1 –4 12 Multiply by –2 Divide by –4 1 –3 –6 < –2 MULTIPLYING INEQUALITIES BY NEGATIVE INTEGERS Words Original Inequality Multiply/ Divide Result Multiplying or dividing by a negative number reverses the inequality symbol.

12 Course Solving Inequalities Containing Integers The direction of the inequality changes only if the number you are using to multiply or divide by is negative. Helpful Hint

13 Course Solving Inequalities Containing Integers A. –3y 15 y –5 Divide each side by –3; changes to. B. 7m < 21 m < 3m < 3 Divide each side by 7. Additional Example 2: Multiplying and Dividing to Solve Inequalities Solve and graph. 0 3–3 5 –3y 15 –3–3–3–3 7m < –7 –5 04

14 15-Feb-14 Solving Inequalities The only one to watch out for is when you are dividing by a negative Example 8 – 3m < 2 -3m < -6 m Subtract 8 from each side Divide across by -3 and change the Sign So m > 2 >

15 15-Feb-14 Solving Inequalities Example 2 5( x – 1 ) - 8x x – 5 – 8x x x - 12 x So x 4

16 Course Solving Inequalities Containing Integers Lesson Quiz: Part 1 Solve and graph. 1. h + 2 < 0 2. c – 5 > –2 7n > 28 t –3 3. < 1 h –2 n > 4 t > –3 c 3 –2– –3–3 0 3 –3–

17 Course Solving Inequalities Containing Integers A local weather forecast stated that it would be 12°F tonight and at least 10° colder the next night. Write an inequality to show how cold it will be ? Lesson Quiz: Part 2 5. x 2°F


Download ppt "2-5 Solving Inequalities Containing Integers Course 3 Lesson Presentation Lesson Presentation."

Similar presentations


Ads by Google