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

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

Solve for x

$$x = -\frac{8}{5} = -1\frac{3}{5} = -1.6$$

Steps for Solving Linear Equation

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

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

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

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Subtract \frac{3}{4}x from both sides.

$$\frac{1}{3}x-\frac{2}{3}-\frac{3}{4}x=0$$

Combine \frac{1}{3}x and -\frac{3}{4}x to get -\frac{5}{12}x.

$$-\frac{5}{12}x-\frac{2}{3}=0$$

Add \frac{2}{3} to both sides. Anything plus zero gives itself.

$$-\frac{5}{12}x=\frac{2}{3}$$

Multiply both sides by -\frac{12}{5}, the reciprocal of -\frac{5}{12}.

$$x=\frac{2}{3}\left(-\frac{12}{5}\right)$$

Multiply \frac{2}{3} times -\frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{2\left(-12\right)}{3\times 5}$$

Do the multiplications in the fraction \frac{2\left(-12\right)}{3\times 5}.

$$x=\frac{-24}{15}$$

Reduce the fraction \frac{-24}{15} to lowest terms by extracting and canceling out 3.

$$x=-\frac{8}{5}$$