Solve 1/2x+3/4(x-2)=1/3(2x-3)

$$\frac{ 1 }{ 2 } x+ \frac{ 3 }{ 4 } (x-2)= \frac{ 1 }{ 3 } (2x-3)$$

Solve for x

$$x=\frac{6}{7}\approx 0.857142857$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{4} by x-2.

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

Express \frac{3}{4}\left(-2\right) as a single fraction.

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

Multiply 3 and -2 to get -6.

$$\frac{1}{2}x+\frac{3}{4}x+\frac{-6}{4}=\frac{1}{3}\left(2x-3\right)$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

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

Combine \frac{1}{2}x and \frac{3}{4}x to get \frac{5}{4}x.

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

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

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

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

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

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

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

Divide -3 by 3 to get -1.

$$\frac{5}{4}x-\frac{3}{2}=\frac{2}{3}x-1$$

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

$$\frac{5}{4}x-\frac{3}{2}-\frac{2}{3}x=-1$$

Combine \frac{5}{4}x and -\frac{2}{3}x to get \frac{7}{12}x.

$$\frac{7}{12}x-\frac{3}{2}=-1$$

Add \frac{3}{2} to both sides.

$$\frac{7}{12}x=-1+\frac{3}{2}$$

Convert -1 to fraction -\frac{2}{2}.

$$\frac{7}{12}x=-\frac{2}{2}+\frac{3}{2}$$

Since -\frac{2}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{7}{12}x=\frac{-2+3}{2}$$

Add -2 and 3 to get 1.

$$\frac{7}{12}x=\frac{1}{2}$$

Multiply both sides by \frac{12}{7}, the reciprocal of \frac{7}{12}.

$$x=\frac{1}{2}\times \frac{12}{7}$$

Multiply \frac{1}{2} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\times 12}{2\times 7}$$

Do the multiplications in the fraction \frac{1\times 12}{2\times 7}.

$$x=\frac{12}{14}$$

Reduce the fraction \frac{12}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{6}{7}$$