Solve 2-1/3(2x-4)=-1/6(x-7)

$$2- \frac{ 1 }{ 3 } (2x-4)=- \frac{ 1 }{ 6 } (x-7)$$

Solve for x

$$x = \frac{13}{3} = 4\frac{1}{3} \approx 4.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{3} by 2x-4.

$$2-\frac{1}{3}\times 2x-\frac{1}{3}\left(-4\right)=-\frac{1}{6}\left(x-7\right)$$

Express -\frac{1}{3}\times 2 as a single fraction.

$$2+\frac{-2}{3}x-\frac{1}{3}\left(-4\right)=-\frac{1}{6}\left(x-7\right)$$

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

$$2-\frac{2}{3}x-\frac{1}{3}\left(-4\right)=-\frac{1}{6}\left(x-7\right)$$

Express -\frac{1}{3}\left(-4\right) as a single fraction.

$$2-\frac{2}{3}x+\frac{-\left(-4\right)}{3}=-\frac{1}{6}\left(x-7\right)$$

Multiply -1 and -4 to get 4.

$$2-\frac{2}{3}x+\frac{4}{3}=-\frac{1}{6}\left(x-7\right)$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{6}{3}-\frac{2}{3}x+\frac{4}{3}=-\frac{1}{6}\left(x-7\right)$$

Since \frac{6}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{6+4}{3}-\frac{2}{3}x=-\frac{1}{6}\left(x-7\right)$$

Add 6 and 4 to get 10.

$$\frac{10}{3}-\frac{2}{3}x=-\frac{1}{6}\left(x-7\right)$$

Use the distributive property to multiply -\frac{1}{6} by x-7.

$$\frac{10}{3}-\frac{2}{3}x=-\frac{1}{6}x-\frac{1}{6}\left(-7\right)$$

Express -\frac{1}{6}\left(-7\right) as a single fraction.

$$\frac{10}{3}-\frac{2}{3}x=-\frac{1}{6}x+\frac{-\left(-7\right)}{6}$$

Multiply -1 and -7 to get 7.

$$\frac{10}{3}-\frac{2}{3}x=-\frac{1}{6}x+\frac{7}{6}$$

Add \frac{1}{6}x to both sides.

$$\frac{10}{3}-\frac{2}{3}x+\frac{1}{6}x=\frac{7}{6}$$

Combine -\frac{2}{3}x and \frac{1}{6}x to get -\frac{1}{2}x.

$$\frac{10}{3}-\frac{1}{2}x=\frac{7}{6}$$

Subtract \frac{10}{3} from both sides.

$$-\frac{1}{2}x=\frac{7}{6}-\frac{10}{3}$$

Least common multiple of 6 and 3 is 6. Convert \frac{7}{6} and \frac{10}{3} to fractions with denominator 6.

$$-\frac{1}{2}x=\frac{7}{6}-\frac{20}{6}$$

Since \frac{7}{6} and \frac{20}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}x=\frac{7-20}{6}$$

Subtract 20 from 7 to get -13.

$$-\frac{1}{2}x=-\frac{13}{6}$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$x=-\frac{13}{6}\left(-2\right)$$

Express -\frac{13}{6}\left(-2\right) as a single fraction.

$$x=\frac{-13\left(-2\right)}{6}$$

Multiply -13 and -2 to get 26.

$$x=\frac{26}{6}$$

Reduce the fraction \frac{26}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{13}{3}$$