Answer:
x ≥ [tex]\frac{21}{5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{5}{18}[/tex] - [tex]\frac{x-2}{9}[/tex] ≤ [tex]\frac{x-4}{6}[/tex]
Multiply through by 18 ( the LCM of 18, 9 and 6 ) to clear the fractions
5 - 2(x - 2) ≤ 3(x - 4) ← distribute parenthesis and simplify
5 - 2x + 4 ≤ 3x - 12
9 - 2x ≤ 3x - 12 ( add 2x to both sides )
9 ≤ 5x - 12 ( add 12 to both sides )
21 ≤ 5x ( divide both sides by 5 )
[tex]\frac{21}{5}[/tex] ≤ x , that is
x ≥ [tex]\frac{21}{5}[/tex]
