Solving Two-Step Inequalities Use the same process when solving two-step inequalities that you used to solve two-step equations.

Solving Two-Step Inequalities Draw an open circle when the inequality includes the < or > symbol. Draw a closed circle when the inequality includes the < or > symbol. Remember!

Example 1: Solving Two-Step Inequalities Solve. Then graph the solution on a number line. 4y – 5 < 11 4y – 5 < 11 + 5 + 5 Add 5 to both sides. 4y < 16 4y < 16 Divide both sides by 4. 4 4 y < 4 º –6 –4 –2 2 4 6

Solving Two-Step Inequalities Example 2 Solve. Then graph the solution on a number line. 2y – 4 > –12 2y – 4 > –12 + 4 + 4 Add 4 to both sides. 2y > –8 2y > –8 Divide both sides by 2. 2 2 y > –4 º –6 –4 –2 2 4 6

Solving Two-Step Inequalities Example 3 Solve. Then graph the solution set on a number line. h 7 + 1 > –1 h 7 + 1 > –1 – 1 – 1 Subtract 1 from both sides. h 7 > –2 h 7 > (7)(–2) (7) Multiply both sides by 7. h > –14 7 14 21 –

Solving Inqualities by Multiplying or Dividing Notes: When you multiply or divide both sides by a negative number, you need to reverse the direction of the inequality symbol.

Solving Two-Step Inequalities Example 4 Solve. Then graph the solution set on a number line. D. –9x + 4 ≤ 31 –9x + 4 ≤ 31 – 4 –4 Subtract 4 from both sides. –9x ≤ 27 Divide both sides by –9, and reverse the inequality symbol. –9x ≥ 27 –9 –9 x ≥ –3 3 6 9 –3 –6 –9

Example 5: Solving Two-Step Inequalities Solve. Then graph the solution set on a number line. m –3 + 8 m –3 5 ≥ + 8 – 8 –8 Subtract 8 from both sides. m –3 -3 ≥ m –3 (–3) ≤ (–3) Multiply both sides by –3, and reverse the inequality symbol. m ≥ 9 • –3 0 3 6 9 12 15

Example 6: Solving Two-Step Inequalities Solve. Then graph the solution set on a number line. y 2 – 6 > 1 y 2 – 6 > 1 + 6 + 6 Add 6 to both sides. y 2 > 7 y 2 > (2)7 (2) Multiply both sides by 2. y > 14 7 14 21 –

Example 7: Solving Two-Step Inequalities Solve. Then graph the solution set on a number line. –4 ≥ –3x + 5 –4 ≥ –3x + 5 – 5 –5 Subtract 5 from both sides. –9 ≤ –3x Divide both sides by –3, and reverse the inequality symbol. –3 –3 x ≥ 3 3 6 9 –3 –6 –9

Solving Two-Step Inequalities Example 8 Solve. Then graph the solution set on a number line. m –2 + 1 ≥ 7 m –2 + 1 ≥ 7 – 1 –1 Subtract 1 from both sides. m –2 ≥ 6 m –2 ≤ (6) (–2) Multiply both sides by –2, and reverse the inequality symbol. m ≤ –12 • –18 –12 –6 0 6 12 18

Solving Two-Step Inequalities Application Sun-Li has $30 to spend at the carnival. Admission is $5, and each ride costs $2. What is the greatest number of rides she can ride? Let r represent the number of rides Sun-Li can ride. 5 + 2r ≤ 30 – 5 –5 Subtract 5 from both sides. 2r ≤ 25 Divide both sides by 2. 2r ≤ 25 2 2 r ≤ 12 252 , or 12 Sun-Li can ride only a whole number of rides, so the most she can ride is 12.

Solving Two-Step Inequalities Application 2 Brice has $30 to take his brother and his friends to the movies. If each ticket costs $4.00, and he must buy tickets for himself and his brother, what is the greatest number of friends he can invite? Let t represent the number of tickets. 8 + 4t ≤ 30 – 8 –8 Subtract 8 from both sides. 4t ≤ 22 Divide both sides by 4. 4t ≤ 22 4 4 t ≤ 5.5 Brice can only buy a whole number of tickets, so the most people he can invite is 5.

Solving Two-Step Inequalities Lesson Quiz: Part I Solve. Then graph each solution set on a number line. –4 –2 2 –6 –8 –10 s > –7 1. 7s + 14 > –35 –62 –60 –58 –56 –64 –66 –68 y < –64 y –8 2. + 12 > 20 2 3 4 5 1 –1 n ≤ 3 3. 18n – 22 ≤ 32

Solving Two-Step Inequalities Lesson Quiz: Part II 4. A cyclist has $7.00. At the first stop on the tour, energy bars are $1.15 each, and a sports drink is $1.75. What is the greatest number of energy bars the cyclist can buy if he buys one sports drink? 4