Solve 5/9x+3/4x=1/6+1/1

$$\frac{ 5 }{ 9 } x+ \frac{ 3 }{ 4 } x= \frac{ 1 }{ 6 } + \frac{ 1 }{ 1 }$$

Solve for x

$$x=\frac{42}{47}\approx 0.893617021$$

Steps for Solving Linear Equation

Combine \frac{5}{9}x and \frac{3}{4}x to get \frac{47}{36}x.

$$\frac{47}{36}x=\frac{1}{6}+\frac{1}{1}$$

Anything divided by one gives itself.

$$\frac{47}{36}x=\frac{1}{6}+1$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{47}{36}x=\frac{1}{6}+\frac{6}{6}$$

Since \frac{1}{6} and \frac{6}{6} have the same denominator, add them by adding their numerators.

$$\frac{47}{36}x=\frac{1+6}{6}$$

Add 1 and 6 to get 7.

$$\frac{47}{36}x=\frac{7}{6}$$

Multiply both sides by \frac{36}{47}, the reciprocal of \frac{47}{36}.

$$x=\frac{7}{6}\times \frac{36}{47}$$

Multiply \frac{7}{6} times \frac{36}{47} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\times 36}{6\times 47}$$

Do the multiplications in the fraction \frac{7\times 36}{6\times 47}.

$$x=\frac{252}{282}$$

Reduce the fraction \frac{252}{282} to lowest terms by extracting and canceling out 6.

$$x=\frac{42}{47}$$