What is the value of x in this equation?
\(\frac{\mathrm{(x+3)} }{\mathrm{4}} = \frac{\mathrm{(2x-3)} }{\mathrm{5}}\)

Always start with the given equation: \(\frac{\mathrm{(x+3)} }{\mathrm{4}} = \frac{\mathrm{(2x-3)} }{\mathrm{5}}\)
Cross-multiply denominators to eliminate each: 5(x+3)=4(2x−3)
Distribute each term through the parentheses: 5x+15=8x–12
Group similar terms by subtracting 5x from both sides, and adding 12 to both sides:
8x−5x=15+12
3x=27
Divide both sides by 3 to solve for x: \(x=27 \div 3=9\)
This answer can be verified by substituting it into the original equation.