(3t-2)/(4)-(2t+3)/(3)=(2)/(3)-t

Find Common Denominator: First, find a common denominator for all terms to eliminate the fractions. Common denominator for 4, 3 is 12. Multiply each term by 12 to clear the fractions: 12 * ((3t-2)/4) - 12 * ((2t+3)/3) = 12 * (2/3) - 12 * tClear Fractions: Simplify each term: (12/4) * (3t-2) - (12/3) * (2t+3) = (12/2) - 12t 3 * (3t-2) - 4 * (2t+3) = 8 - 12tSimplify Terms: Distribute and combine like terms: 9t - 6 - 8t - 12 = 8 - 12t t - 18 = 8 - 12tCombine Like Terms: Add 12t to both sides to get all t terms on one side: t + 12t - 18 = 8 13t - 18 = 8Isolate Term with t: Add 18 to both sides to isolate the term with t: 13t = 26Solve for t: Divide both sides by 13 to solve for t: t = 26 / 13 t = 2

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Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

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

Find Common Denominator: First, find a common denominator for all terms to eliminate the fractions. $\newline$ Common denominator for $4, 3$ is $12$ . $\newline$ Multiply each term by $12$ to clear the fractions: $\newline$ $12 \times \left(\frac{3t-2}{4}\right) - 12 \times \left(\frac{2t+3}{3}\right) = 12 \times \left(\frac{2}{3}\right) - 12 \times t$
Clear Fractions: Simplify each term: $\newline$ $(\frac{12}{4}) \cdot (3t-2) - (\frac{12}{3}) \cdot (2t+3) = (\frac{12}{2}) - 12t$ $\newline$ $3 \cdot (3t-2) - 4 \cdot (2t+3) = 6 - 12t$
Simplify Terms: Distribute and combine like terms: $\newline$ $9t - 6 - 8t - 12 = 8 - 12t$ $\newline$ $t - 18 = 8 - 12t$
Combine Like Terms: Add $12t$ to both sides to get all $t$ terms on one side: $\newline$ $t + 12t - 18 = 8$ $\newline$ $13t - 18 = 8$
Isolate Term with $t$ : Add $18$ to both sides to isolate the term with $t$ : $13t = 26$
Solve for t: Divide both sides by $13$ to solve for t: $\newline$ t = $\frac{26}{13}$ $\newline$ t = $2$