Example 1A: Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. y ≤ 4y + 18 y ≤ 4y + 18 –y –y 0 ≤ 3y + 18 To collect the variable terms on one side, subtract y from both sides. Since 18 is added to 3y, subtract 18 from both sides to undo the addition. –18 – 18 –18 ≤ 3y Since y is multiplied by 3, divide both sides by 3 to undo the multiplication. –6 ≤ y (or y  –6) –10 –8 –6 –4 –2 2 4 6 8 10

Example 1B: Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. 4m – 3 < 2m + 6 To collect the variable terms on one side, subtract 2m from both sides. –2m – 2m 2m – 3 < + 6 Since 3 is subtracted from 2m, add 3 to both sides to undo the subtraction + 3 + 3 2m < 9 Since m is multiplied by 2, divide both sides by 2 to undo the multiplication. 4 5 6

Lesson Quiz: Part III Solve each inequality. 5. 2y – 2 ≥ 2(y + 7) no solutions 6. 2(–6r – 5) < –3(4r + 2) all real numbers