Problem of the Week

Updated at Sep 27, 2021 1:30 PM

This week's problem comes from the equation category.

How can we solve the equation \(\frac{4}{5}t-\frac{t-3}{5}=3\)?

Let's begin!



\[\frac{4}{5}t-\frac{t-3}{5}=3\]

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

2
Join the denominators.
\[\frac{4t-(t-3)}{5}=3\]

3
Remove parentheses.
\[\frac{4t-t+3}{5}=3\]

4
Simplify  \(4t-t+3\)  to  \(3t+3\).
\[\frac{3t+3}{5}=3\]

5
Factor out the common term \(3\).
\[\frac{3(t+1)}{5}=3\]

6
Multiply both sides by \(5\).
\[3(t+1)=3\times 5\]

7
Simplify  \(3\times 5\)  to  \(15\).
\[3(t+1)=15\]

8
Divide both sides by \(3\).
\[t+1=\frac{15}{3}\]

9
Simplify  \(\frac{15}{3}\)  to  \(5\).
\[t+1=5\]

10
Subtract \(1\) from both sides.
\[t=5-1\]

11
Simplify  \(5-1\)  to  \(4\).
\[t=4\]

Done
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