Question 15 Solve the given inequality for real x: x/4 < (5x-2)/3 - (7x-3)/5
Class X1 - Maths -Linear Inequalities Page 122
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x/4 < (5x -2)/3 - (7x -3)/5
x/4 < {5(5x - 2) -3(7x - 3)}/15
x/4 < {25x -10 -21x +9 }/15
x/4 < (4x -1 )/15
15x < 4( 4x -1)
15x < 16x - 4
subtract 16x both sides,
15x - 16x < 16x - 16x - 4
- x < - 4
multiply with (-1) both sides, sign of inequality will be change .
x > 4 hence, x∈(4,∞)
x/4 < {5(5x - 2) -3(7x - 3)}/15
x/4 < {25x -10 -21x +9 }/15
x/4 < (4x -1 )/15
15x < 4( 4x -1)
15x < 16x - 4
subtract 16x both sides,
15x - 16x < 16x - 16x - 4
- x < - 4
multiply with (-1) both sides, sign of inequality will be change .
x > 4 hence, x∈(4,∞)
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