Question 16 Solve the given inequality for real x: (2x-1)/3 ≥ (3x-2)/4 - (2-x)/5
Class X1 - Maths -Linear Inequalities Page 122
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(2x -1)/3 ≥ (3x -2)/4 - (2 - x)/5
(2x -1)/3 ≥ [5(3x - 2) -4( 2 - x)]/20
(2x - 1)/3 ≥ [ 15x -10 - 8 +4x ]/20
(2x - 1)/3 ≥ (19x - 18 )/20
multiply with 60 both sides,
(2x -1)/3 × 60 ≥ (19x - 18)/20 × 60
(2x - 1) × 20 ≥ (19x -18) × 3
40x - 20 ≥ 57x - 54
subtract 57x both sides,
40x -57x - 20 ≥ 57x - 57x - 54
-17x - 20 ≥ -54
-17x ≥ -54 + 20 = -34
divide by (-17) both sides, sign of inequality will be change .
x ≤ 2 hence, x∈(-∞, 2]
(2x -1)/3 ≥ [5(3x - 2) -4( 2 - x)]/20
(2x - 1)/3 ≥ [ 15x -10 - 8 +4x ]/20
(2x - 1)/3 ≥ (19x - 18 )/20
multiply with 60 both sides,
(2x -1)/3 × 60 ≥ (19x - 18)/20 × 60
(2x - 1) × 20 ≥ (19x -18) × 3
40x - 20 ≥ 57x - 54
subtract 57x both sides,
40x -57x - 20 ≥ 57x - 57x - 54
-17x - 20 ≥ -54
-17x ≥ -54 + 20 = -34
divide by (-17) both sides, sign of inequality will be change .
x ≤ 2 hence, x∈(-∞, 2]
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