Question 10 Solve the given inequality for real x: x/3 > x/2 + 1
Class X1 - Maths -Linear Inequalities Page 122
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★ LINEAR INEQUALITIES ★
REDUCING LINEAR INEQUALITIES AT THEIR MAXIMUM EXTENT HERE , AND IN OTHER FEW CASES ; GENERALITY HAS BEEN USED UPTO PROPER EXTENDS
AS BEING CAREFUL WHILE CHOOSING INTEGRAL SOLUTIONS OF THE RESPECTIVE INEQUALITY
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
REDUCING LINEAR INEQUALITIES AT THEIR MAXIMUM EXTENT HERE , AND IN OTHER FEW CASES ; GENERALITY HAS BEEN USED UPTO PROPER EXTENDS
AS BEING CAREFUL WHILE CHOOSING INTEGRAL SOLUTIONS OF THE RESPECTIVE INEQUALITY
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
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x/3 > x/2 + 1
subtract x/2 both sides,
[ equal number may be subtracted from both sides of an inequality without affecting the sign of inequality. ]
now,
x/3 - x/2 > x/2 + 1 - x/2
x{1/3 - 1/2 } > 1
x{(2 - 3)/6 } > 1
x{ (-1/6)} > 1
-x/6 > 1
multiply with -6 both sides, sign of inequality will be change .
x <-6 , hence x € ( -∞, -6)
in number line :
-∞___________-5____-6____∞
-------------------------------------()
subtract x/2 both sides,
[ equal number may be subtracted from both sides of an inequality without affecting the sign of inequality. ]
now,
x/3 - x/2 > x/2 + 1 - x/2
x{1/3 - 1/2 } > 1
x{(2 - 3)/6 } > 1
x{ (-1/6)} > 1
-x/6 > 1
multiply with -6 both sides, sign of inequality will be change .
x <-6 , hence x € ( -∞, -6)
in number line :
-∞___________-5____-6____∞
-------------------------------------()
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