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### Middle/High School Algebra, Geometry, and Statistics (AGS)2.12 Solving Inequations - II

 Example: Solve 2(x+3) < 5 (x-3). Solution: 2x+6 < 5x-15. Add -6 to both sides, we get 2x + 6 - 6 < 5x - 15 -6 2x < 5x - 21 Add -5x to both sides, we get 2x - 5x < 5x -21 -5x -3x < -21 Divide both sides by -3. -3x/-3 > -21/-3 x > 7 \ Any number > 7 is a solution. Verification: Substituting x = 8 > 7 L.H.S. = 2(x+3) = 2(8+3) = 2*11 = 22 R.H.S. = 5(x-3) = 5(8-3) = 5 * 5 = 25 \ 22 < 25 \ 8 > 7 is a root. Similarly we can show that any number greater than 7 is a root. Directions: Solve the following inequality. Also write at least ten examples of your own.
 Q 1: Solve 5(x + 4) < 9(x - 4).x < 14x > 15x > 14x < 13 Q 2: Solve 4(x + 2) < 6(x - 2).x > 10x < 8x < 10x > 5 Q 3: Solve 5(x + 2) < 7(x - 2).x < 15x > 12x > 20x < 12 Q 4: Solve 2(x + 7) < 9(x - 7).x > 4x < 11x > 11x < 5 Q 5: Solve 4(x + 3) < 7(x - 3).x > 1x < 11x > 11x < 6 Q 6: Solve 2(x + 4) < 6(x - 4).x > 0x < 0x > 8x < 8 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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