Solve 3/4:frac{sqrt{7}}{4}:x=4:5:6

$$\frac { 3 } { 4 } : \frac { \sqrt { 7 } } { 4 } : x = 4 : 5 : 6$$

Solve for x

$$x = \frac{45 \sqrt{7}}{14} \approx 8.504200643$$

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 6x, the least common multiple of x,6.

$$6\times \frac{\frac{3}{4}}{\frac{\sqrt{7}}{4}}=x\times \frac{4}{5}$$

Divide \frac{3}{4} by \frac{\sqrt{7}}{4} by multiplying \frac{3}{4} by the reciprocal of \frac{\sqrt{7}}{4}.

$$6\times \frac{3\times 4}{4\sqrt{7}}=x\times \frac{4}{5}$$

Cancel out 4 in both numerator and denominator.

$$6\times \frac{3}{\sqrt{7}}=x\times \frac{4}{5}$$

Rationalize the denominator of \frac{3}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$6\times \frac{3\sqrt{7}}{\left(\sqrt{7}\right)^{2}}=x\times \frac{4}{5}$$

The square of \sqrt{7} is 7.

$$6\times \frac{3\sqrt{7}}{7}=x\times \frac{4}{5}$$

Express 6\times \frac{3\sqrt{7}}{7} as a single fraction.

$$\frac{6\times 3\sqrt{7}}{7}=x\times \frac{4}{5}$$

Multiply 6 and 3 to get 18.

$$\frac{18\sqrt{7}}{7}=x\times \frac{4}{5}$$

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

$$x\times \frac{4}{5}=\frac{18\sqrt{7}}{7}$$

Multiply both sides of the equation by 35, the least common multiple of 5,7.

$$35x\times \frac{4}{5}=5\times 18\sqrt{7}$$

Reorder the terms.

$$\frac{4}{5}\times 35x=5\times 18\sqrt{7}$$

Express \frac{4}{5}\times 35 as a single fraction.

$$\frac{4\times 35}{5}x=5\times 18\sqrt{7}$$

Multiply 4 and 35 to get 140.

$$\frac{140}{5}x=5\times 18\sqrt{7}$$

Divide 140 by 5 to get 28.

$$28x=5\times 18\sqrt{7}$$

Multiply 5 and 18 to get 90.

$$28x=90\sqrt{7}$$

Divide both sides by 28.

$$\frac{28x}{28}=\frac{90\sqrt{7}}{28}$$

Dividing by 28 undoes the multiplication by 28.

$$x=\frac{90\sqrt{7}}{28}$$

Divide 90\sqrt{7} by 28.

$$x=\frac{45\sqrt{7}}{14}$$