Solve 30/42:x=5/6:7/6

$$\frac { 30 } { 42 } : x = \frac { 5 } { 6 } : \frac { 7 } { 6 }$$

Solve for x

$$x=1$$

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.

$$\frac{30}{42}=x\times \frac{\frac{5}{6}}{\frac{7}{6}}$$

Reduce the fraction \frac{30}{42} to lowest terms by extracting and canceling out 6.

$$\frac{5}{7}=x\times \frac{\frac{5}{6}}{\frac{7}{6}}$$

Divide \frac{5}{6} by \frac{7}{6} by multiplying \frac{5}{6} by the reciprocal of \frac{7}{6}.

$$\frac{5}{7}=x\times \frac{5}{6}\times \frac{6}{7}$$

Multiply \frac{5}{6} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{7}=x\times \frac{5\times 6}{6\times 7}$$

Cancel out 6 in both numerator and denominator.

$$\frac{5}{7}=x\times \frac{5}{7}$$

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

$$x\times \frac{5}{7}=\frac{5}{7}$$

Multiply both sides by \frac{7}{5}, the reciprocal of \frac{5}{7}.

$$x=\frac{5}{7}\times \frac{7}{5}$$

Cancel out \frac{5}{7} and its reciprocal \frac{7}{5}.

$$x=1$$