Solve 7/bc=9/14,4

$$\frac { 7 } { b c } = \frac { 9 } { 14,4 }$$

Solve for b

$$b=\frac{56}{5c}$$

$$c\neq 0$$

Steps for Solving Linear Equation

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

$$7=bc\times \frac{9}{14,4}$$

Expand \frac{9}{14,4} by multiplying both numerator and the denominator by 10.

$$7=bc\times \frac{90}{144}$$

Reduce the fraction \frac{90}{144} to lowest terms by extracting and canceling out 18.

$$7=bc\times \frac{5}{8}$$

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

$$bc\times \frac{5}{8}=7$$

The equation is in standard form.

$$\frac{5c}{8}b=7$$

Divide both sides by \frac{5}{8}c.

$$\frac{8\times \frac{5c}{8}b}{5c}=\frac{7\times 8}{5c}$$

Dividing by \frac{5}{8}c undoes the multiplication by \frac{5}{8}c.

$$b=\frac{7\times 8}{5c}$$

Divide 7 by \frac{5}{8}c.

$$b=\frac{56}{5c}$$

Variable b cannot be equal to 0.

$$b=\frac{56}{5c}\text{, }b\neq 0$$

Solve for c

$$c=\frac{56}{5b}$$

$$b\neq 0$$

Steps for Solving Linear Equation

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

$$7=bc\times \frac{9}{14,4}$$

Expand \frac{9}{14,4} by multiplying both numerator and the denominator by 10.

$$7=bc\times \frac{90}{144}$$

Reduce the fraction \frac{90}{144} to lowest terms by extracting and canceling out 18.

$$7=bc\times \frac{5}{8}$$

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

$$bc\times \frac{5}{8}=7$$

The equation is in standard form.

$$\frac{5b}{8}c=7$$

Divide both sides by \frac{5}{8}b.

$$\frac{8\times \frac{5b}{8}c}{5b}=\frac{7\times 8}{5b}$$

Dividing by \frac{5}{8}b undoes the multiplication by \frac{5}{8}b.

$$c=\frac{7\times 8}{5b}$$

Divide 7 by \frac{5}{8}b.

$$c=\frac{56}{5b}$$

Variable c cannot be equal to 0.

$$c=\frac{56}{5b}\text{, }c\neq 0$$