Problem of the Week

Updated at Jan 22, 2024 8:44 AM

To get more practice in equation, we brought you this problem of the week:

How would you solve \(\frac{\frac{4}{5}z-3}{3}=-\frac{11}{15}\)?

Check out the solution below!



\[\frac{\frac{4}{5}z-3}{3}=-\frac{11}{15}\]

1
Simplify  \(\frac{4}{5}z\)  to  \(\frac{4z}{5}\).
\[\frac{\frac{4z}{5}-3}{3}=-\frac{11}{15}\]

2
Simplify  \(\frac{\frac{4z}{5}-3}{3}\)  to  \(-1+\frac{\frac{4z}{5}}{3}\).
\[-1+\frac{\frac{4z}{5}}{3}=-\frac{11}{15}\]

3
Simplify  \(\frac{\frac{4z}{5}}{3}\)  to  \(\frac{4z}{5\times 3}\).
\[-1+\frac{4z}{5\times 3}=-\frac{11}{15}\]

4
Simplify  \(5\times 3\)  to  \(15\).
\[-1+\frac{4z}{15}=-\frac{11}{15}\]

5
Regroup terms.
\[\frac{4z}{15}-1=-\frac{11}{15}\]

6
Add \(1\) to both sides.
\[\frac{4z}{15}=-\frac{11}{15}+1\]

7
Simplify  \(-\frac{11}{15}+1\)  to  \(\frac{4}{15}\).
\[\frac{4z}{15}=\frac{4}{15}\]

8
Multiply both sides by \(15\).
\[4z=\frac{4}{15}\times 15\]

9
Cancel \(15\).
\[4z=4\]

10
Divide both sides by \(4\).
\[z=1\]

Done
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