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)×55z=−84(z-3)\times \frac{5}{5z}=-8?

Let's begin!



4(z−3)×55z=−84(z-3)\times \frac{5}{5z}=-8

1
Cancel 55.
4(z−3)×1z=−84(z-3)\times \frac{1}{z}=-8

2
Simplify  4(z−3)×1z4(z-3)\times \frac{1}{z}  to  4(z−3)z\frac{4(z-3)}{z}.
4(z−3)z=−8\frac{4(z-3)}{z}=-8

3
Multiply both sides by zz.
4(z−3)=−8z4(z-3)=-8z

4
Divide both sides by 44.
z−3=−2zz-3=-2z

5
Subtract zz from both sides.
−3=−2z−z-3=-2z-z

6
Simplify  −2z−z-2z-z  to  −3z-3z.
−3=−3z-3=-3z

7
Divide both sides by −3-3.
1=z1=z

8
Switch sides.
z=1z=1

Done
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