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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 inequality. When graphing inequalities on a number line, use solid circles ( ) for  and  and open circles ( ) for > and <. k +3 > –2.

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Learn to solve inequalities with integers.

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  1. Inequalities & Integers Learn to solve inequalities with integers.

  2. 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  and open circles ( ) for > and <.

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

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

  5. –5 < 1 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 5 > –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 5 is greater than –1. –1 • 5 –1 • (–1) Multiply both sides by –1. –51 > or < ? –5< 1 You know –5 is less than 1, so you should use <.

  6. MULTIPLYING INEQUALITIES BY NEGATIVE INTEGERS Original Inequality Multiply/Divide Words Result Multiplying or dividing by a negative number reversesthe inequality symbol. 3 > 1 –6 < –2 Multiply by –2 –4  12 1  –3 Divide by –4

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

  8. –3y 15 –3 –3 –5 –7 0 4 7m < 21 7 7 0 5 –3 3 Solve and graph. A. –3y 15 Divide each side by –3;  changes to . y–5 B. 7m < 21 Divide each side by 7. m<3

  9. –2 0 2 –3 3 0 t –3 –3 3 0 0 8 4 Solve and graph. 1.h + 2 < 0 h–2 2. c– 5 > –2 c 3 3. < 1 t > –3 4. 7n > 28 n > 4

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

  11. 0 8 0 x t -4 0 8 4 -8 0 Two-step Inequalities. Solve and graph. 1.-1 + 2m > 15 n8 2. -5k + 1 > 21 k < -4 -4 3. + 5 > 4 t-4 4. + 1> 0 x -8

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