Problem of the Week

Updated at Feb 5, 2024 2:05 PM

This week's problem comes from the equation category.

How would you solve \(4(z-3)\times \frac{5}{5z}=-8\)?

Let's begin!



\[4(z-3)\times \frac{5}{5z}=-8\]

1
Cancel \(5\).
\[4(z-3)\times \frac{1}{z}=-8\]

2
Simplify  \(4(z-3)\times \frac{1}{z}\)  to  \(\frac{4(z-3)}{z}\).
\[\frac{4(z-3)}{z}=-8\]

3
Multiply both sides by \(z\).
\[4(z-3)=-8z\]

4
Divide both sides by \(4\).
\[z-3=-2z\]

5
Subtract \(z\) from both sides.
\[-3=-2z-z\]

6
Simplify  \(-2z-z\)  to  \(-3z\).
\[-3=-3z\]

7
Divide both sides by \(-3\).
\[1=z\]

8
Switch sides.
\[z=1\]

Done
Cymath foriOSAndroid