Learn to solve inequalities with integers. Inequalities & 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!

k > –5 A. k +3 > –2 Subtract 3 from both sides. –3 k +3 > –2 Solve and graph. –5 0

B. r – 9  12 r  21 Add 9 to both sides. r –  r – 9  Solve and graph.

–5 1 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

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.

The direction of the inequality changes only if the number you are using to multiply or divide by is negative. Helpful Hint

A. –3y  15 y  –5 Divide each side by –3;  changes to . B. 7m < 21 m < 3m < 3 Divide each side by 7. Solve and graph. 0 3–3 5 –3y  15 –3–3–3–3 7m < –7 –5 04

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–

Solve and graph – 2n > – 2r < –6 + 5 < 6 x 5 3. – 1 > 1 n  –2 r < 6 x  10 r > 1 –2– r 6 Two-step Inequalities.

Solve and graph m > k + 1 > > 0 t > 4 n  8n  8 x  -8 t  -4 k < x 8 -4 Two-step Inequalities.