Solve 1/6(x-7)=1/7(6-x)

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

Solve for x

$$x = \frac{85}{13} = 6\frac{7}{13} \approx 6.538461538$$

Steps for Solving Linear Equation

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

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

Multiply \frac{1}{6} and -7 to get \frac{-7}{6}.

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

Fraction \frac{-7}{6} can be rewritten as -\frac{7}{6} by extracting the negative sign.

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

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

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

Multiply \frac{1}{7} and 6 to get \frac{6}{7}.

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

Multiply \frac{1}{7} and -1 to get -\frac{1}{7}.

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

Add \frac{1}{7}x to both sides.

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

Combine \frac{1}{6}x and \frac{1}{7}x to get \frac{13}{42}x.

$$\frac{13}{42}x-\frac{7}{6}=\frac{6}{7}$$

Add \frac{7}{6} to both sides.

$$\frac{13}{42}x=\frac{6}{7}+\frac{7}{6}$$

Least common multiple of 7 and 6 is 42. Convert \frac{6}{7} and \frac{7}{6} to fractions with denominator 42.

$$\frac{13}{42}x=\frac{36}{42}+\frac{49}{42}$$

Since \frac{36}{42} and \frac{49}{42} have the same denominator, add them by adding their numerators.

$$\frac{13}{42}x=\frac{36+49}{42}$$

Add 36 and 49 to get 85.

$$\frac{13}{42}x=\frac{85}{42}$$

Multiply both sides by \frac{42}{13}, the reciprocal of \frac{13}{42}.

$$x=\frac{85}{42}\times \frac{42}{13}$$

Multiply \frac{85}{42} times \frac{42}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{85\times 42}{42\times 13}$$

Cancel out 42 in both numerator and denominator.

$$x=\frac{85}{13}$$