Module 6 topic 2 notes
- 1. Multiple Step Inequalities Go from 7x +4 > 3x – 12 To x > -4
- 2. Using More Than One Step Solve 7 + 6a > 19. Check the solution. 7 + 6a > 19 -7 - 7 Isolate 6a by subtracting 7 6a > 12 a > 2 Divide each side by 6. ‘a’ is by itself
- 3. Using the Distributive Property Solve 2(t + 2) – 3t ≥ -1. 2(t + 2) – 3t ≥ -1 Distribute the 2 to t + 2 2t + 4 – 3t ≥ -1 Combine 2t and -3t the like terms. -t + 4 ≥ -1 - 4 -4 Subtract 4 from each side. -t ≥ -5 Divide each side by –1 and switch the t ≤ 5 inequality sign.
- 4. Solving Inequalities with Variables on Both Sides Gathering Variables on One Side of an Inequality. Solve 6z – 15 < 4z + 11. 6z – 15 < 4z + 11 -4z -4z Move the smaller ‘z’ term by subtracting 4z 2z – 15 < 11 + 15 +15 Isolate 2z by adding 15 2z < 26 Divide both sides by 2 so z is by itself. z < 13
- 5. Multi-Step Inequalities Solve -3(4 – m) ≥ 4 (2m + 1) . -3(4 – m) ≥ 4 (2m + 1) -12 + 3m ≥ 8m + 4 Distribute –3 and 4 on each side - 8m - 8m Move the ‘m’ terms both to the left side. -12 – 5m ≥ 4 +12 +12 Add 12 to isolate –5m -5m ≥ 16 Divide both sides by –5. Switch the inequality since 5 is negative. Change fraction to a mixed number.
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