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Home : Math & Science : Math Study Guides : Algebra I : Compound Inequalities : Compound Inequalities
Compound Inequalities To solve a compound inequality, first separate it into two inequalities. Determine whether the answer should be a union of sets ("or") or an intersection of sets ("and"). Then, solve both inequalities and graph. If it is unclear whether the inequality is a union of sets or an intersection of sets, then ##test each region## to see if it satisfies the compound inequality. Example 1: Solve and graph: 4≤2x≤8 4≤2x and 2x≤8 (intersection of sets) 4≤2x ≤![]() 2≤x x≥2 ≤82x≤4 Graph: Example 1 Example 2: Solve and graph: {x : 5≤ +5 < 6}5≤ + 5 and +5 < 6 (intersection of sets)5≤ + 5 0≤ ![]() 0≤x +5 < 6 < 1x < 3 Graph: Example 2 Example 3: Solve and graph: 3(x - 2) < 9 or 3(x - 2) > 15 (union of sets) 3(x - 2) < 9 x - 2 < 3 3(x - 2) > 15x < 5 x - 2 > 5 x < 5 or x > 7.x > 7 Graph: Example 3 Example 4: Solve and graph: {x : 2x≤x - 3}∪{x : x < 3x - 4} 2x≤x - 3 or x < 3x - 4 (union of sets) 2x≤x - 3 x≤ - 3 x < 3x - 4 -2x < - 4 x≤ - 3 or x > 2.x >2 Graph: Example 4 Example 5: Solve and graph: 2x - 2 < - 2 or 3(x + 5) > 2x + 15 (union of sets) 2x - 2 < - 2 2x < 0 3(x + 5) > 2x + 15x < 0 3x + 15 > 2x + 15 x < 0 or x > 0.3x > 2x x > 0 Graph: Example 5 Example 6: 2x - 3 < 5≤2 - 3x 2x - 3 < 5 and 5≤2 - 3x (intersection of sets) 2x - 3 < 5 2x < 8 5≤2 - 3xx < 4 3≤ - 3x -1≥x x≤ - 1 x < 4 and x≤ - 1.Graph: Example 6 |
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