Question that was on practice diploma.

800/x - 800/6x = 8

sorry i posted this again. i didnt understand the steps given. i was told to multiply it by 2000/3x or something similar. i need it either in a more basic more detailed procedure.

I asume \(\begin{array}{rcl} \frac{800}{x} - \frac{800}{6x} &=& 8 \end{array}\)

\(\begin{array}{rcll} \frac{800}{x} - \frac{800}{6x} &=& 8 \\\\ \frac{800}{x} - \frac{800}{x}\cdot \frac16 &=& 8 \\\\ \frac{800}{x} \cdot \left( 1 - \frac16 \right) &=& 8 \\\\ \frac{800}{x} \cdot \left( \frac66 - \frac16 \right) &=& 8 \\\\ \frac{800}{x} \cdot \left( \frac56 \right) &=& 8 \qquad & |\qquad \cdot x \\\\ 800 \cdot \left( \frac56 \right) &=& 8\cdot x \qquad & |\qquad :8 \\\\ \frac{800}{8} \cdot \left( \frac56 \right) &=& x \\\\ 100 \cdot \left( \frac56 \right) &=& x \\\\ \frac{500}{6} &=& x \\\\ 83.3333333333\dots &=& x \\\\ \mathbf{x} & \mathbf{=} & \mathbf{83\frac13} \\\\ \end{array}\)

800/x - 800/6x = 8, What is the GCD of x and 6x? it is 6x, so

[4800 - 800] / 6x=8

4000/6x=8 cross multiply

4000=48x divide both sides by 48

x=4000/48

x=83 1/3= 250/3