Solve 1/10.5+1/q=r/10

$$\frac { 1 } { 10.5 } + \frac { 1 } { q } = \frac { r } { 10 }$$

Solve for q

$$q=\frac{210}{21r-20}$$

$$r\neq \frac{20}{21}$$

Steps for Solving Linear Equation

Variable q cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10q, the least common multiple of q,10.

$$10q\times \frac{1}{10.5}+10=qr$$

Expand \frac{1}{10.5} by multiplying both numerator and the denominator by 10.

$$10q\times \frac{10}{105}+10=qr$$

Reduce the fraction \frac{10}{105} to lowest terms by extracting and canceling out 5.

$$10q\times \frac{2}{21}+10=qr$$

Multiply 10 and \frac{2}{21} to get \frac{20}{21}.

$$\frac{20}{21}q+10=qr$$

Subtract qr from both sides.

$$\frac{20}{21}q+10-qr=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$\frac{20}{21}q-qr=-10$$

Combine all terms containing q.

$$\left(\frac{20}{21}-r\right)q=-10$$

Divide both sides by \frac{20}{21}-r.

$$\frac{\left(\frac{20}{21}-r\right)q}{\frac{20}{21}-r}=-\frac{10}{\frac{20}{21}-r}$$

Dividing by \frac{20}{21}-r undoes the multiplication by \frac{20}{21}-r.

$$q=-\frac{10}{\frac{20}{21}-r}$$

Divide -10 by \frac{20}{21}-r.

$$q=-\frac{210}{20-21r}$$

Variable q cannot be equal to 0.

$$q=-\frac{210}{20-21r}\text{, }q\neq 0$$

Solve for r

$$r=\frac{20}{21}+\frac{10}{q}$$

$$q\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10q, the least common multiple of q,10.

$$10q\times \frac{1}{10.5}+10=qr$$

Expand \frac{1}{10.5} by multiplying both numerator and the denominator by 10.

$$10q\times \frac{10}{105}+10=qr$$

Reduce the fraction \frac{10}{105} to lowest terms by extracting and canceling out 5.

$$10q\times \frac{2}{21}+10=qr$$

Multiply 10 and \frac{2}{21} to get \frac{20}{21}.

$$\frac{20}{21}q+10=qr$$

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

$$qr=\frac{20}{21}q+10$$

The equation is in standard form.

$$qr=\frac{20q}{21}+10$$

Divide both sides by q.

$$\frac{qr}{q}=\frac{\frac{20q}{21}+10}{q}$$

Dividing by q undoes the multiplication by q.

$$r=\frac{\frac{20q}{21}+10}{q}$$

Divide \frac{20q}{21}+10 by q.

$$r=\frac{20}{21}+\frac{10}{q}$$