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Solve the equation: 3/(t−2) = 4/(3t+4)

April 6, 2026Mathematics

ScanSolve AI Answer

Answer

t = -4

5 steps

Here's the solution to the problem:

The problem is to solve the equation:

\frac{3}{t-2} = \frac{4}{3t+4}

Cross-multiply to eliminate the denominators.
$3(3t+4) = 4(t-2)$
Distribute the numbers into the parentheses.
$3 \times 3t + 3 \times 4 = 4 \times t - 4 \times 2$ $9t + 12 = 4t - 8$
Rearrange the equation to gather terms with $t$ on one side and constant terms on the other.
Subtract $4t$ from both sides.
$9t - 4t + 12 = -8$
Subtract 12 from both sides.
$5t = -8 - 12$
Combine like terms.
$5t = -20$
Solve for $t$ by dividing both sides by 5.
$t = \frac{-20}{5}$ $t = -4$

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