Solve 5/6*x+8+x=5/6+4*x+2/3

$$\frac { 5 } { 6 } \cdot x + 8 + x = \frac { 5 } { 6 } + 4 \cdot x + \frac { 2 } { 3 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Combine \frac{5}{6}x and x to get \frac{11}{6}x.

$$\frac{11}{6}x+8=\frac{5}{6}+4x+\frac{2}{3}$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{2}{3} to fractions with denominator 6.

$$\frac{11}{6}x+8=\frac{5}{6}+4x+\frac{4}{6}$$

Since \frac{5}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{11}{6}x+8=\frac{5+4}{6}+4x$$

Add 5 and 4 to get 9.

$$\frac{11}{6}x+8=\frac{9}{6}+4x$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{11}{6}x+8=\frac{3}{2}+4x$$

Subtract 4x from both sides.

$$\frac{11}{6}x+8-4x=\frac{3}{2}$$

Combine \frac{11}{6}x and -4x to get -\frac{13}{6}x.

$$-\frac{13}{6}x+8=\frac{3}{2}$$

Subtract 8 from both sides.

$$-\frac{13}{6}x=\frac{3}{2}-8$$

Convert 8 to fraction \frac{16}{2}.

$$-\frac{13}{6}x=\frac{3}{2}-\frac{16}{2}$$

Since \frac{3}{2} and \frac{16}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{6}x=\frac{3-16}{2}$$

Subtract 16 from 3 to get -13.

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

Multiply both sides by -\frac{6}{13}, the reciprocal of -\frac{13}{6}.

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

Multiply -\frac{13}{2} times -\frac{6}{13} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-13\left(-6\right)}{2\times 13}.

$$x=\frac{78}{26}$$

Divide 78 by 26 to get 3.

$$x=3$$