Lesson 2 4 Objective To solve multistep inequalities

Lesson: 2. 4 Objective: To solve multi-step inequalities Essential Question: How do I solve multi-step inequality? Example #1: solving multi-step inequalities 2 x − 4 ≥ 8 + 4 +4 2 x ≥ 12 2 2 x≥ 6 Add 4 to both sides. Divide both sides by 2. Solution Set Check: 2( 6 ) - 4 ≥ 8 8≥ 8

Example: solving an inequality with variables on both sides 6 x − 5 < 2 x + 11 – 2 x 4 x − 5 < 11 +5 +5 4 x < 16 4 4 x<4 Check: Subtract 2 x from both sides. Add 5 to both sides Divide both sides by 4 Solutions set: all real numbers less than 4 6(3) − 5 < 2(3) + 11 18 − 5 < 6 + 11 13 < 17 ✓ Checks

Example #2: Distribute the 8 on the left and 12 on the right of the inequality 24 g – 16 ≤ 24 g + 12 – 24 g Subtract 24 g from both sides. – 24 g − 16 ≤ 12 Solution set is the set of all real numbers. This type of inequality is also called an…. ? Identity

Example #3: 2(-4 s + 2) ≥ -5 s − 10 -8 s + 4 ≥ -5 s − 10 +5 s − 3 s + 4 ≥ − 10 − 4 − 3 s ≥ − 14 − 3 14 s≤ 3 Distribute the 2 on the left side of the inequality Add 5 s to both sides. Minus 4 from both sides. Divide both sides by − 3 (Remember to switch the direction of the inequality) Solution Set

Real Life Problems – Modeling with Mathematics Example #5: solve and graph You have scored 20 points on the homework, 20 points on the class work, and have 10 points from the last quiz. The coming test is worth 100 points. Your grade will be based on a total possible points of 175. What would you have to get on the test to get at least a “C” in the class? Total points 50 Test Score + x + ≥ ≥ 50 + x ≥ 175 *. 70 50 + x ≥ 122. 5 x ≥ 72. 5 Possible 70% Score. 70 Points 175 * Complete multiplication Minus 50 from both sides 71 72 73 74 75

Write a summary about the difference between solving multi-step equations and multi-step inequalities.