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Learn to solve inequalities with integers. Inequalities & Integers

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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!

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

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B. r – 9 12 r 21 Add 9 to both sides. r – 9 + 9 12 + 9 r – 9 12 21 24 15 Solve and graph.

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–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 –1 0 1 2 3 4 5 6 7 –5 < 1 5 > –1

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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.

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

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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 < 21 7 7 –7 –5 04

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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 –2–2 02 3 –3–3 0 3 –3–3 0 4 8 0 4.

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Solve and graph. 1. -3 – 2n > 1 2. -4 – 2r < –6 + 5 < 6 x 5 3. – 1 > 1 n –2 r < 6 x 10 r > 1 –2–2 02 0 10 0 6 9 0 4. r 6 Two-step Inequalities.

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Solve and graph. 1. -1 + 2m > 15 2. -5k + 1 > 21 + 1 > 0 t 4 3. + 5 > 4 n 8n 8 x -8 t -4 k < -4 0 8 0 -4 0 0 - 8 4. x 8 -4 Two-step Inequalities.

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