Solve 3x-11-1/6(7x+8)=x-4

$$3 x - 11 - \frac { 1 } { 6 } ( 7 x + 8 ) = x - 4$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{6} by 7x+8.

$$3x-11-\frac{1}{6}\times 7x-\frac{1}{6}\times 8=x-4$$

Express -\frac{1}{6}\times 7 as a single fraction.

$$3x-11+\frac{-7}{6}x-\frac{1}{6}\times 8=x-4$$

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

$$3x-11-\frac{7}{6}x-\frac{1}{6}\times 8=x-4$$

Express -\frac{1}{6}\times 8 as a single fraction.

$$3x-11-\frac{7}{6}x+\frac{-8}{6}=x-4$$

Reduce the fraction \frac{-8}{6} to lowest terms by extracting and canceling out 2.

$$3x-11-\frac{7}{6}x-\frac{4}{3}=x-4$$

Combine 3x and -\frac{7}{6}x to get \frac{11}{6}x.

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

Convert -11 to fraction -\frac{33}{3}.

$$\frac{11}{6}x-\frac{33}{3}-\frac{4}{3}=x-4$$

Since -\frac{33}{3} and \frac{4}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{6}x+\frac{-33-4}{3}=x-4$$

Subtract 4 from -33 to get -37.

$$\frac{11}{6}x-\frac{37}{3}=x-4$$

Subtract x from both sides.

$$\frac{11}{6}x-\frac{37}{3}-x=-4$$

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

$$\frac{5}{6}x-\frac{37}{3}=-4$$

Add \frac{37}{3} to both sides.

$$\frac{5}{6}x=-4+\frac{37}{3}$$

Convert -4 to fraction -\frac{12}{3}.

$$\frac{5}{6}x=-\frac{12}{3}+\frac{37}{3}$$

Since -\frac{12}{3} and \frac{37}{3} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}x=\frac{-12+37}{3}$$

Add -12 and 37 to get 25.

$$\frac{5}{6}x=\frac{25}{3}$$

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

$$x=\frac{25}{3}\times \frac{6}{5}$$

Multiply \frac{25}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{25\times 6}{3\times 5}$$

Do the multiplications in the fraction \frac{25\times 6}{3\times 5}.

$$x=\frac{150}{15}$$

Divide 150 by 15 to get 10.

$$x=10$$