Solve 3/4*(u-3)=1/3*(2u-5)

$$\frac { 3 } { 4 } \cdot ( u - 3 ) = \frac { 1 } { 3 } \cdot ( 2 u - 5 )$$

Solve for u

$$u=7$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{4} by u-3.

$$\frac{3}{4}u+\frac{3}{4}\left(-3\right)=\frac{1}{3}\left(2u-5\right)$$

Express \frac{3}{4}\left(-3\right) as a single fraction.

$$\frac{3}{4}u+\frac{3\left(-3\right)}{4}=\frac{1}{3}\left(2u-5\right)$$

Multiply 3 and -3 to get -9.

$$\frac{3}{4}u+\frac{-9}{4}=\frac{1}{3}\left(2u-5\right)$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$\frac{3}{4}u-\frac{9}{4}=\frac{1}{3}\left(2u-5\right)$$

Use the distributive property to multiply \frac{1}{3} by 2u-5.

$$\frac{3}{4}u-\frac{9}{4}=\frac{1}{3}\times 2u+\frac{1}{3}\left(-5\right)$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{3}{4}u-\frac{9}{4}=\frac{2}{3}u+\frac{1}{3}\left(-5\right)$$

Multiply \frac{1}{3} and -5 to get \frac{-5}{3}.

$$\frac{3}{4}u-\frac{9}{4}=\frac{2}{3}u+\frac{-5}{3}$$

Fraction \frac{-5}{3} can be rewritten as -\frac{5}{3} by extracting the negative sign.

$$\frac{3}{4}u-\frac{9}{4}=\frac{2}{3}u-\frac{5}{3}$$

Subtract \frac{2}{3}u from both sides.

$$\frac{3}{4}u-\frac{9}{4}-\frac{2}{3}u=-\frac{5}{3}$$

Combine \frac{3}{4}u and -\frac{2}{3}u to get \frac{1}{12}u.

$$\frac{1}{12}u-\frac{9}{4}=-\frac{5}{3}$$

Add \frac{9}{4} to both sides.

$$\frac{1}{12}u=-\frac{5}{3}+\frac{9}{4}$$

Least common multiple of 3 and 4 is 12. Convert -\frac{5}{3} and \frac{9}{4} to fractions with denominator 12.

$$\frac{1}{12}u=-\frac{20}{12}+\frac{27}{12}$$

Since -\frac{20}{12} and \frac{27}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{12}u=\frac{-20+27}{12}$$

Add -20 and 27 to get 7.

$$\frac{1}{12}u=\frac{7}{12}$$

Multiply both sides by 12, the reciprocal of \frac{1}{12}.

$$u=\frac{7}{12}\times 12$$

Cancel out 12 and 12.

$$u=7$$