Problem of the Week

Updated at Feb 4, 2019 2:47 PM

How would you solve \(\frac{\frac{t-3}{3}+2}{3}=\frac{8}{9}\)?

Below is the solution.



\[\frac{\frac{t-3}{3}+2}{3}=\frac{8}{9}\]

1
Simplify \(\frac{t-3}{3}\) to \(-1+\frac{t}{3}\).
\[\frac{-1+\frac{t}{3}+2}{3}=\frac{8}{9}\]

2
Simplify \(-1+\frac{t}{3}+2\) to \(\frac{t}{3}+1\).
\[\frac{\frac{t}{3}+1}{3}=\frac{8}{9}\]

3
Simplify \(\frac{\frac{t}{3}+1}{3}\) to \(\frac{\frac{t}{3}}{3}+\frac{1}{3}\).
\[\frac{\frac{t}{3}}{3}+\frac{1}{3}=\frac{8}{9}\]

4
Simplify \(\frac{\frac{t}{3}}{3}\) to \(\frac{t}{3\times 3}\).
\[\frac{t}{3\times 3}+\frac{1}{3}=\frac{8}{9}\]

5
Simplify \(3\times 3\) to \(9\).
\[\frac{t}{9}+\frac{1}{3}=\frac{8}{9}\]

6
Subtract \(\frac{1}{3}\) from both sides.
\[\frac{t}{9}=\frac{8}{9}-\frac{1}{3}\]

7
Simplify \(\frac{8}{9}-\frac{1}{3}\) to \(\frac{5}{9}\).
\[\frac{t}{9}=\frac{5}{9}\]

8
Multiply both sides by \(9\).
\[t=\frac{5}{9}\times 9\]

9
Simplify \(\frac{5}{9}\times 9\) to \(\frac{45}{9}\).
\[t=\frac{45}{9}\]

10
Simplify \(\frac{45}{9}\) to \(5\).
\[t=5\]

Done