Solve 5/7xdiv5/14=7/8

$$\frac { 5 } { 7 x } \div \frac { 5 } { 14 } = \frac { 7 } { 8 }$$

Solve for x

$$x = \frac{16}{7} = 2\frac{2}{7} \approx 2.285714286$$

Steps for Solving Linear Equation

Multiply both sides by \frac{5}{14}.

$$\frac{5}{7x}=\frac{7}{8}\times \frac{5}{14}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 56x, the least common multiple of 7x,8,14.

$$8\times 5=\frac{7}{8}\times \frac{5}{14}\times 56x$$

Multiply 8 and 5 to get 40.

$$40=\frac{7}{8}\times \frac{5}{14}\times 56x$$

Multiply \frac{7}{8} and \frac{5}{14} to get \frac{5}{16}.

$$40=\frac{5}{16}\times 56x$$

Multiply \frac{5}{16} and 56 to get \frac{35}{2}.

$$40=\frac{35}{2}x$$

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

$$\frac{35}{2}x=40$$

Multiply both sides by \frac{2}{35}, the reciprocal of \frac{35}{2}.

$$x=40\times \frac{2}{35}$$

Multiply 40 and \frac{2}{35} to get \frac{16}{7}.

$$x=\frac{16}{7}$$