Lesson Objective: I will be able to … Solve one-step inequalities in one variable by using multiplication using division Language Objective: I will be able to … Read, write, and listen about vocabulary, key concepts, and examples

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Example 1: Multiplying or Dividing by a Positive Number Page 15 Solve the inequality 7x > -42 and graph the solutions. > Since x is multiplied by 7, divide both sides by 7 to undo the multiplication. 1x > –6 x > –6 –10 –8 –6 –4 –2 2 4 6 8 10

Example 2: Multiplying or Dividing by a Positive Number Page 16 Solve the inequality and graph the solutions. Since r is multiplied by , multiply both sides by the reciprocal of . r < 16 2 4 6 8 10 12 14 16 18 20

Solve the inequality and graph the solutions. Your Turn 2 Page 16 Solve the inequality and graph the solutions. Since m is divided by 3, multiply both sides by 3 to undo the division. 3(2.4) ≤ 3 7.2 ≤ m (or m ≥ 7.2) 2 4 6 8 10 12 14 16 18 20

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Important! If you multiply or divide of an inequality by a negative number, you must reverse the inequality to make the statement true. Example: Solve the inequality -12x > 84. Divide both sides by -12. > x > -7 Check solution: x can equal -5 since -5 > -7. -12(-5) > 84 60 > 84, but this is FALSE! Since x was divided by a negative number, we must change > to <. So x < –7 is the answer.

Caution! Do not change the direction of the inequality symbol just because you see a negative sign. For example, you do not change the symbol when solving 4x < –24.

Example 3: Multiplying or Dividing by a Negative Number Page 16 Solve the inequality and graph the solutions. Since x is divided by –3, multiply both sides by –3. Change to . 24  x (or x  24) 16 18 20 22 24 10 14 26 28 30 12

Solve the inequality 10 ≥ -x and graph the solutions. Your Turn 3 Page 17 Solve the inequality 10 ≥ -x and graph the solutions. –1(10) ≥ –1(–x) Multiply both sides by –1 to make x positive. Change  to . –10 ≤ x –10 –8 –6 –4 –2 2 4 6 8 10

Homework Assignment #4 Holt 3-3 #5-10, 42, 57-60