Answer
The solution is $x = 17$.
Work Step by Step
The first thing we want to do is get rid of the fractions. We do this by multiplying both sides by the denominator(s) of the fraction(s) we want to eliminate:
$2x + 5 = 3x - 12$
Collect constants on the right side of the equation:
$-x = -17$
Divide both sides by $-1$:
$x = 17$
The solution is $x = 17$.
To check our answer, we plug the value into the original equation.
$\frac{2(17) + 5}{17 - 7} = \frac{3(17) - 12}{17 - 7}$
Simplify numerators and denominators:
$\frac{39}{10} = \frac{39}{10}$
Both sides of the equation are equal. Therefore, this solution is correct.
