Answer:
x = - 15
Step-by-step explanation:
Given
[tex]\frac{x}{5}[/tex] = 5 + [tex]\frac{x-9}{3}[/tex]
Multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions
3x = 75 + 5(x - 9) ← distribute and simplify right side
3x = 75 + 5x - 45
3x = 5x + 30 ( subtract 5x from both sides )
- 2x = 30 ( divide both sides by - 2 )
x = - 15
As a check
substitute x = - 15 into the equation and if both sides are equal then it is the solution.
left side = [tex]\frac{-15}{5}[/tex] = - 3
right side = 5 + [tex]\frac{-15-9}{3}[/tex] = 5 + [tex]\frac{-24}{3}[/tex] = 5 - 8 = - 3
Thus x = - 15 is the solution
