# Objective: To solve multi-step inequalities Essential Question: How do I solve multi-step inequality? Example #1 : solving multi-step inequalities 2x −

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Objective: To solve multi-step inequalities Essential Question: How do I solve multi-step inequality? Example #1 : solving multi-step inequalities 2x − 4 ≥ 8Add 4 to both sides. + 4 +4 2x ≥ 12Divide both sides by 2. 2 2 x ≥ 6 Solution Set Check: 2( 6 ) - 4 ≥ 8 8 ≥ 8 Lesson: 2.4

Example: solving an inequality with variables on both sides 6x − 5 < 2x + 11Subtract 2x from both sides. – 2x 4x − 5 < 11 Add 5 to both sides + 5 + 5 4x < 16 Divide both sides by 4 4 x < 4 Solutions set: all real numbers less than 4 Check: 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 24g – 16 ≤ 24g + 12 Subtract 24g from both sides. – 24g −16 ≤ 12 Solution set is the set of all real numbers. This type of inequality is also called an….?

Example #3: Distribute the 2 on the left side of the inequality Add 5s to both sides. +5s −3s + 4 ≥ −10 2(-4s + 2) ≥ -5s − 10 -8s + 4 ≥ -5s − 10 Minus 4 from both sides. −4 −3s ≥ −14Divide both sides by −3 −3 (Remember to switch the direction of the inequality) s ≤ 3 14 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 Test Score ≥ Possible Points 70% Score 50 + x ≥ 175 *.70 Complete multiplication 50 + x ≥ 122.5 Minus 50 from both sides x ≥ 72.5 + 71 72 73 74 75

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

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