Solve (2+4/6)divx=(3+3/9)div(5-1/2)

$$(2+ \frac{ 4 }{ 6 } ) \div x=(3+ \frac{ 3 }{ 9 } ) \div (5- \frac{ 1 }{ 2 } )$$

Solve for x

$$x = \frac{18}{5} = 3\frac{3}{5} = 3.6$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$2+\frac{4}{6}=\frac{2}{9}x\left(3+\frac{3}{9}\right)$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$2+\frac{2}{3}=\frac{2}{9}x\left(3+\frac{3}{9}\right)$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{6}{3}+\frac{2}{3}=\frac{2}{9}x\left(3+\frac{3}{9}\right)$$

Since \frac{6}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{6+2}{3}=\frac{2}{9}x\left(3+\frac{3}{9}\right)$$

Add 6 and 2 to get 8.

$$\frac{8}{3}=\frac{2}{9}x\left(3+\frac{3}{9}\right)$$

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

$$\frac{8}{3}=\frac{2}{9}x\left(3+\frac{1}{3}\right)$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{8}{3}=\frac{2}{9}x\left(\frac{9}{3}+\frac{1}{3}\right)$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{8}{3}=\frac{2}{9}x\times \frac{9+1}{3}$$

Add 9 and 1 to get 10.

$$\frac{8}{3}=\frac{2}{9}x\times \frac{10}{3}$$

Multiply \frac{2}{9} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{3}=\frac{2\times 10}{9\times 3}x$$

Do the multiplications in the fraction \frac{2\times 10}{9\times 3}.

$$\frac{8}{3}=\frac{20}{27}x$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{20}{27}x=\frac{8}{3}$$

Multiply both sides by \frac{27}{20}, the reciprocal of \frac{20}{27}.

$$x=\frac{8}{3}\times \frac{27}{20}$$

Multiply \frac{8}{3} times \frac{27}{20} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{8\times 27}{3\times 20}$$

Do the multiplications in the fraction \frac{8\times 27}{3\times 20}.

$$x=\frac{216}{60}$$

Reduce the fraction \frac{216}{60} to lowest terms by extracting and canceling out 12.

$$x=\frac{18}{5}$$