Solve 11x-10=(11x-1)5/6

$$11 x - 10 = ( 11 x - 1 ) \frac { 5 } { 6 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 11x-1 by \frac{5}{6}.

$$11x-10=11x\times \frac{5}{6}-\frac{5}{6}$$

Express 11\times \frac{5}{6} as a single fraction.

$$11x-10=\frac{11\times 5}{6}x-\frac{5}{6}$$

Multiply 11 and 5 to get 55.

$$11x-10=\frac{55}{6}x-\frac{5}{6}$$

Subtract \frac{55}{6}x from both sides.

$$11x-10-\frac{55}{6}x=-\frac{5}{6}$$

Combine 11x and -\frac{55}{6}x to get \frac{11}{6}x.

$$\frac{11}{6}x-10=-\frac{5}{6}$$

Add 10 to both sides.

$$\frac{11}{6}x=-\frac{5}{6}+10$$

Convert 10 to fraction \frac{60}{6}.

$$\frac{11}{6}x=-\frac{5}{6}+\frac{60}{6}$$

Since -\frac{5}{6} and \frac{60}{6} have the same denominator, add them by adding their numerators.

$$\frac{11}{6}x=\frac{-5+60}{6}$$

Add -5 and 60 to get 55.

$$\frac{11}{6}x=\frac{55}{6}$$

Multiply both sides by \frac{6}{11}, the reciprocal of \frac{11}{6}.

$$x=\frac{55}{6}\times \frac{6}{11}$$

Multiply \frac{55}{6} times \frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{55\times 6}{6\times 11}$$

Cancel out 6 in both numerator and denominator.

$$x=\frac{55}{11}$$

Divide 55 by 11 to get 5.

$$x=5$$