Solve 2/3-1/6+1/16x=1/3-frac{1}{4}x

$$\frac { 2 } { 3 } - \frac { 1 } { 6 } + \frac { 1 } { 16 } x = \frac { 1 } { 3 } - \frac { 1 } { 4 } x$$

Solve for x

$$x=-\frac{8}{15}\approx -0.533333333$$

Steps for Solving Linear Equation

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{4}{6}-\frac{1}{6}+\frac{1}{16}x=\frac{1}{3}-\frac{1}{4}x$$

Since \frac{4}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-1}{6}+\frac{1}{16}x=\frac{1}{3}-\frac{1}{4}x$$

Subtract 1 from 4 to get 3.

$$\frac{3}{6}+\frac{1}{16}x=\frac{1}{3}-\frac{1}{4}x$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}+\frac{1}{16}x=\frac{1}{3}-\frac{1}{4}x$$

Add \frac{1}{4}x to both sides.

$$\frac{1}{2}+\frac{1}{16}x+\frac{1}{4}x=\frac{1}{3}$$

Combine \frac{1}{16}x and \frac{1}{4}x to get \frac{5}{16}x.

$$\frac{1}{2}+\frac{5}{16}x=\frac{1}{3}$$

Subtract \frac{1}{2} from both sides.

$$\frac{5}{16}x=\frac{1}{3}-\frac{1}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{5}{16}x=\frac{2}{6}-\frac{3}{6}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{16}x=\frac{2-3}{6}$$

Subtract 3 from 2 to get -1.

$$\frac{5}{16}x=-\frac{1}{6}$$

Multiply both sides by \frac{16}{5}, the reciprocal of \frac{5}{16}.

$$x=-\frac{1}{6}\times \frac{16}{5}$$

Multiply -\frac{1}{6} times \frac{16}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-16}{6\times 5}$$

Do the multiplications in the fraction \frac{-16}{6\times 5}.

$$x=\frac{-16}{30}$$

Reduce the fraction \frac{-16}{30} to lowest terms by extracting and canceling out 2.

$$x=-\frac{8}{15}$$