Transformation of an equation with a fraction in the numerator of a fraction

Question

Can someone explain the steps here -- how does it get the second part where it is equals to $20$? I was confused because of the fraction $1/2$ in the numerator.

I am studying some examples but I don't understand this one. \begin{gather*} \frac{(1/2)x}{21} + \frac{(1/2)x}{24} = 10\\ \frac{x}{21} + \frac{x}{24} = 20\\ 15 x = 168 \times 20 \end{gather*}

Answer 1

1) Given:

$$\dfrac{(1/2)x}{21}+ \dfrac {(1/2)x}{24} = 10$$

2) We have the same equation as:

$$\dfrac{0.5x}{21}+\dfrac{0.5x}{24} = 10$$

3) To get: $$\dfrac{x}{21}+\dfrac{x}{24} = 20$$

4) Simply multiply the entire equation in step 2) by 2:

$$2\left(\dfrac{0.5x}{21}+\dfrac{0.5x}{24} = 10\right)$$

5) We are left with: $$\dfrac{x}{21}+\dfrac{x}{24} = 20$$

Answer 2

If you have $$ \frac{(1/2)x}{21}+\frac{(1/2)x}{24}=10 $$ then you can take a factor of $\frac{1}{2}$ out the front of the left-hand side $$ \frac{1}{2}\left(\frac{x}{21}+\frac{x}{24}\right)=10 $$ and then multiply both sides of the equation by $2$ $$ \frac{x}{21}+\frac{x}{24}=20 $$