Question

Solve the following linear in-equation and graph the solution set on a real number line: 

${\displaystyle \frac{1}{3}(5\text{x}-8)\ge \frac{1}{2}(4\text{x}-7)}$, x ∈ R

Answer 1

${\displaystyle \frac{1}{3}(5\text{x}-8)\ge \frac{1}{2}(4\text{x}-7)}$

2(5x - 8) ≥ 3 (4x - 7)

10x - 16 ≥ 12x - 21

10x - 12x ≥ -21 + 16

-2x ≥ -5

x ≤ ${\displaystyle \frac{5}{2}}$

x ≤ ${\displaystyle 2\frac{1}{2}}$

Solution set = ${\displaystyle [\text{x}\le 2\frac{1}{2}]}$