Solve 5-7/5/frac{24{7}sqrt{2}}=x/5+frac{7{5}}

$$\frac { 5 - \frac { 7 } { 5 } } { \frac { 24 } { 7 } \sqrt { 2 } } = \frac { x } { 5 + \frac { 7 } { 5 } }$$

Solve for x

$$x = \frac{84 \sqrt{2}}{25} \approx 4.75175757$$

Steps for Solving Linear Equation

Convert 5 to fraction \frac{25}{5}.

$$\frac{\frac{25}{5}-\frac{7}{5}}{\frac{24}{7}\sqrt{2}}=\frac{x}{5+\frac{7}{5}}$$

Since \frac{25}{5} and \frac{7}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25-7}{5}}{\frac{24}{7}\sqrt{2}}=\frac{x}{5+\frac{7}{5}}$$

Subtract 7 from 25 to get 18.

$$\frac{\frac{18}{5}}{\frac{24}{7}\sqrt{2}}=\frac{x}{5+\frac{7}{5}}$$

Express \frac{\frac{18}{5}}{\frac{24}{7}\sqrt{2}} as a single fraction.

$$\frac{18}{5\times \frac{24}{7}\sqrt{2}}=\frac{x}{5+\frac{7}{5}}$$

Rationalize the denominator of \frac{18}{5\times \frac{24}{7}\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{18\sqrt{2}}{5\times \frac{24}{7}\left(\sqrt{2}\right)^{2}}=\frac{x}{5+\frac{7}{5}}$$

The square of \sqrt{2} is 2.

$$\frac{18\sqrt{2}}{5\times \frac{24}{7}\times 2}=\frac{x}{5+\frac{7}{5}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{9\sqrt{2}}{\frac{24}{7}\times 5}=\frac{x}{5+\frac{7}{5}}$$

Express \frac{24}{7}\times 5 as a single fraction.

$$\frac{9\sqrt{2}}{\frac{24\times 5}{7}}=\frac{x}{5+\frac{7}{5}}$$

Multiply 24 and 5 to get 120.

$$\frac{9\sqrt{2}}{\frac{120}{7}}=\frac{x}{5+\frac{7}{5}}$$

Divide 9\sqrt{2} by \frac{120}{7} to get \frac{21}{40}\sqrt{2}.

$$\frac{21}{40}\sqrt{2}=\frac{x}{5+\frac{7}{5}}$$

Convert 5 to fraction \frac{25}{5}.

$$\frac{21}{40}\sqrt{2}=\frac{x}{\frac{25}{5}+\frac{7}{5}}$$

Since \frac{25}{5} and \frac{7}{5} have the same denominator, add them by adding their numerators.

$$\frac{21}{40}\sqrt{2}=\frac{x}{\frac{25+7}{5}}$$

Add 25 and 7 to get 32.

$$\frac{21}{40}\sqrt{2}=\frac{x}{\frac{32}{5}}$$

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

$$\frac{x}{\frac{32}{5}}=\frac{21}{40}\sqrt{2}$$

The equation is in standard form.

$$\frac{5}{32}x=\frac{21\sqrt{2}}{40}$$

Divide both sides of the equation by \frac{5}{32}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{32}x}{\frac{5}{32}}=\frac{21\sqrt{2}}{\frac{5}{32}\times 40}$$

Dividing by \frac{5}{32} undoes the multiplication by \frac{5}{32}.

$$x=\frac{21\sqrt{2}}{\frac{5}{32}\times 40}$$

Divide \frac{21\sqrt{2}}{40} by \frac{5}{32} by multiplying \frac{21\sqrt{2}}{40} by the reciprocal of \frac{5}{32}.

$$x=\frac{84\sqrt{2}}{25}$$