Inequalities Integers Learn to solve inequalities with integers

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Inequalities & Integers Learn to solve inequalities with integers.

Inequalities & Integers Learn to solve inequalities with integers.

Remember! The graph of an inequality shows all of the numbers that satisfy the

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 > –

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

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

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

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

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;

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

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 –

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

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