Question

Question 12 Solve the given inequality for real x: [3x/5 + 4]/2 ≥ (x-6)/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

(3x/5 + 4)/2 ≥ (x - 6)/3
multiply with 6 both sides,
(3x/5 + 4)/2 × 6 ≥ (x -6)/3 × 6
3(3x + 20)/5 ≥ (x -6) × 2

Again, multiply with 5 both sides,

3(3x + 20)/5 × 5 ≥2(x -6) × 5
3(3x + 20) ≥ 10(x - 6)
9x + 60 ≥ 10x - 60
subtract 10x from both sides,
9x -10x + 60 ≥ 10x -60 -10x
-x + 60 ≥ -60
-x ≥ -60 -60
-x ≥ -120

multiply with (-1) both sides, sign of inequality will be changed .
x ≤ 120