Solve c-1/5*(1/2x-4/3x)=25

$$c \frac { - 1 } { 5 } \cdot ( \frac { 1 } { 2 } x - \frac { 4 } { 3 } x ) = 25$$

Solve for c

$$c=\frac{150}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$c\left(-\frac{1}{5}\right)\left(\frac{1}{2}x-\frac{4}{3}x\right)=25$$

Combine \frac{1}{2}x and -\frac{4}{3}x to get -\frac{5}{6}x.

$$c\left(-\frac{1}{5}\right)\left(-\frac{5}{6}\right)x=25$$

Multiply -\frac{1}{5} and -\frac{5}{6} to get \frac{1}{6}.

$$c\times \frac{1}{6}x=25$$

The equation is in standard form.

$$\frac{x}{6}c=25$$

Divide both sides by \frac{1}{6}x.

$$\frac{6\times \frac{x}{6}c}{x}=\frac{6\times 25}{x}$$

Dividing by \frac{1}{6}x undoes the multiplication by \frac{1}{6}x.

$$c=\frac{6\times 25}{x}$$

Divide 25 by \frac{1}{6}x.

$$c=\frac{150}{x}$$

Solve for x

$$x=\frac{150}{c}$$

$$c\neq 0$$

Steps for Solving Linear Equation

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$c\left(-\frac{1}{5}\right)\left(\frac{1}{2}x-\frac{4}{3}x\right)=25$$

Combine \frac{1}{2}x and -\frac{4}{3}x to get -\frac{5}{6}x.

$$c\left(-\frac{1}{5}\right)\left(-\frac{5}{6}\right)x=25$$

Multiply -\frac{1}{5} and -\frac{5}{6} to get \frac{1}{6}.

$$c\times \frac{1}{6}x=25$$

The equation is in standard form.

$$\frac{c}{6}x=25$$

Divide both sides by \frac{1}{6}c.

$$\frac{6\times \frac{c}{6}x}{c}=\frac{6\times 25}{c}$$

Dividing by \frac{1}{6}c undoes the multiplication by \frac{1}{6}c.

$$x=\frac{6\times 25}{c}$$

Divide 25 by \frac{1}{6}c.

$$x=\frac{150}{c}$$