Question

Question 7 Solve the given inequality for real x: 3(x – 1) ≤ 2 (x – 3)

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

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Answer 2

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