Solve 4/3+x/6=x

$$\frac { 4 } { 3 } + \frac { x } { 6 } = x$$

Solve for x

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

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 6 is 6. Multiply \frac{4}{3} times \frac{2}{2}.

$$\frac{4\times 2}{6}+\frac{x}{6}=x$$

Since \frac{4\times 2}{6} and \frac{x}{6} have the same denominator, add them by adding their numerators.

$$\frac{4\times 2+x}{6}=x$$

Do the multiplications in 4\times 2+x.

$$\frac{8+x}{6}=x$$

Divide each term of 8+x by 6 to get \frac{4}{3}+\frac{1}{6}x.

$$\frac{4}{3}+\frac{1}{6}x=x$$

Subtract x from both sides.

$$\frac{4}{3}+\frac{1}{6}x-x=0$$

Combine \frac{1}{6}x and -x to get -\frac{5}{6}x.

$$\frac{4}{3}-\frac{5}{6}x=0$$

Subtract \frac{4}{3} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{5}{6}x=-\frac{4}{3}$$

Multiply both sides by -\frac{6}{5}, the reciprocal of -\frac{5}{6}.

$$x=-\frac{4}{3}\left(-\frac{6}{5}\right)$$

Multiply -\frac{4}{3} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-4\left(-6\right)}{3\times 5}$$

Do the multiplications in the fraction \frac{-4\left(-6\right)}{3\times 5}.

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

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

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