Inequalities Integers Learn to solve inequalities with integers
- Slides: 11
Inequalities & Integers Learn to solve inequalities with integers.
Remember! 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 open circles ( ) for > and <.
Solve and graph. A. k +3 > – 2 – 3 k > – 5 Subtract 3 from both sides. 0
Solve and graph. B. r – 9 12 r – 9 + 9 12 + 9 Add 9 to both sides. r 21 15 21 24
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 5 is greater than – 1 • 5 – 1 • (– 1) Multiply both sides by – 1. – 5 1 > or < ? – 5 < 1 You know – 5 is less than 1, so you should use <. – 5 < 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 5 > – 1
MULTIPLYING INEQUALITIES BY NEGATIVE INTEGERS Words Multiplying or dividing by a negative number reverses the inequality symbol. Original Inequality Multiply/ Divide Result 3>1 Multiply by – 2 – 6 < – 2 – 4 12 Divide by – 4 1 – 3
Helpful Hint The direction of the inequality changes only if the number you are using to multiply or divide by is negative.
Solve and graph. A. – 3 y 15 Divide each side by – 3; changes to . – 3 y 15 – 3 – 7 – 5 0 y – 5 B. 7 m < 21 7 7 m<3 Divide each side by 7. – 3 0 3 5 4
Solve and graph. 1. h + 2 < 0 h – 2 0 2 2. c – 5 > – 2 3. 4. c 3 – 3 0 3 t <1 – 3 t > – 3 0 3 0 4 7 n > 28 n>4 8
Two-step Inequalities. Solve and graph. 1. -3 – 2 n > 1 n – 2 0 2 2. -4 – 2 r < – 6 0 r>1 3. 4. x 5 – 1>1 x 10 r +5<6 6 r < 6 0 0 10 6 9
Two-step Inequalities. Solve and graph. 1. -1 + 2 m > 15 n 8 0 8 2. -5 k + 1 > 21 k < -4 3. 4. t 4 -4 0 +5>4 t -4 x +1>0 8 x -8 -8 0
- Kinetic learning
- Solving rational equations and inequalities
- Solving inequalities with variables on both sides
- How to solve linear inequalities word problems
- Solving systems of inequalities by graphing
- Lesson 8 solve two step inequalities
- How to solve rational inequalities algebraically
- Exponential and logarithmic inequalities
- Solve linear inequalities graphically
- Lesson 1-6 compound inequalities
- Solve by graphing