Question

Question 11 Solve the given inequality for real x: [(3(x-2)/5)] ≤ [5(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

★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★

Answer 2

[3(x - 2)/5 ] ≤ [ 5(2 - x)/3 ]
multiply with 15 both sides,

3(x -2)/5 × 15 ≤ 5( 2 - x)/3 × 15
3(x -2)× 3 ≤5( 2 - x) × 5
9( x -2) ≤ 25(2 - x)
9x - 18 ≤ 50 - 25x
add 25x both sides,
[ equal number may be subtracted from both sides of an inequality without affecting the sign of inequality. ]
now,
9x +25x - 18 ≤ 50
34x ≤ 50 + 18
34x ≤ 68
divide by 34 both sides,
x ≤ 2