Solve 3/4-x+6/11=5/6x

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

Solve for x

$$x=\frac{171}{242}\approx 0.70661157$$

Steps for Solving Linear Equation

Least common multiple of 4 and 11 is 44. Convert \frac{3}{4} and \frac{6}{11} to fractions with denominator 44.

$$\frac{33}{44}-x+\frac{24}{44}=\frac{5}{6}x$$

Since \frac{33}{44} and \frac{24}{44} have the same denominator, add them by adding their numerators.

$$\frac{33+24}{44}-x=\frac{5}{6}x$$

Add 33 and 24 to get 57.

$$\frac{57}{44}-x=\frac{5}{6}x$$

Subtract \frac{5}{6}x from both sides.

$$\frac{57}{44}-x-\frac{5}{6}x=0$$

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

$$\frac{57}{44}-\frac{11}{6}x=0$$

Subtract \frac{57}{44} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{11}{6}x=-\frac{57}{44}$$

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

$$x=-\frac{57}{44}\left(-\frac{6}{11}\right)$$

Multiply -\frac{57}{44} times -\frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-57\left(-6\right)}{44\times 11}$$

Do the multiplications in the fraction \frac{-57\left(-6\right)}{44\times 11}.

$$x=\frac{342}{484}$$

Reduce the fraction \frac{342}{484} to lowest terms by extracting and canceling out 2.

$$x=\frac{171}{242}$$