Question

Question 8 Solve the given inequality for real x: 3(2 – x) ≥ 2(1 – x)

Class X1 - Maths -Linear Inequalities Page 122

Answer 1

★ 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

★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★

Answer 2

3( 2 - x) ≥ 2( 1 - x)
=> 6 - 3x ≥ 2 - 2x
subtract 6 both sides,
6 -3x -6 ≥ 2 - 2x - 6
=> -3x ≥ -2x -4
add 2x both sides,
[ equal number may be added to both sides of an inequality without affecting the sign of inequality. ]
now,
-3x + 2x ≥ -2x +2x - 4
-x ≥ -4
multiply (-1) with both sides,
-x.(-1) ≤ -4.(-1)
x ≤ 4 , hence , x€ (-∞, 4]
in number line ,
-∞--------------1----2----3----4--------------∞
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