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Solve the proportion: (6x+5)/(2x−5) = (3x−4)/(x-3)

August 20, 2026Mathematics

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Answer

x = \frac{7}{2}

4 steps

Cross-multiply the terms in the proportion.
$(6x+5)(x-3) = (3x-4)(2x-5)$
Expand both sides of the equation.
$6x^2 - 18x + 5x - 15 = 6x^2 - 15x - 8x + 20$ $6x^2 - 13x - 15 = 6x^2 - 23x + 20$
Subtract $6x^2$ from both sides and rearrange the terms to isolate $x$ .
$-13x - 15 = -23x + 20$
Add $23x$ to both sides:
$-13x + 23x - 15 = 20$ $10x - 15 = 20$
Add 15 to both sides:
$10x = 20 + 15$ $10x = 35$
Solve for $x$ .
$x = \frac{35}{10}$ $x = \frac{7}{2}$