Problem of the Week

Updated at Sep 15, 2025 5:16 PM

For this week we've brought you this equation problem.

How would you solve the equation \(2(w-3)\times \frac{5}{4w}=\frac{5}{8}\)?

Here are the steps:



\[2(w-3)\times \frac{5}{4w}=\frac{5}{8}\]

1
Simplify  \(2(w-3)\times \frac{5}{4w}\)  to  \(\frac{10(w-3)}{4w}\).
\[\frac{10(w-3)}{4w}=\frac{5}{8}\]

2
Simplify  \(\frac{10(w-3)}{4w}\)  to  \(\frac{5(w-3)}{2w}\).
\[\frac{5(w-3)}{2w}=\frac{5}{8}\]

3
Multiply both sides by \(2w\).
\[5(w-3)=\frac{5}{8}\times 2w\]

4
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[5(w-3)=\frac{5\times 2w}{8}\]

5
Simplify  \(5\times 2w\)  to  \(10w\).
\[5(w-3)=\frac{10w}{8}\]

6
Simplify  \(\frac{10w}{8}\)  to  \(\frac{5w}{4}\).
\[5(w-3)=\frac{5w}{4}\]

7
Multiply both sides by \(4\).
\[20(w-3)=5w\]

8
Divide both sides by \(5\).
\[4(w-3)=w\]

9
Expand.
\[4w-12=w\]

10
Subtract \(4w\) from both sides.
\[-12=w-4w\]

11
Simplify  \(w-4w\)  to  \(-3w\).
\[-12=-3w\]

12
Divide both sides by \(-3\).
\[\frac{-12}{-3}=w\]

13
Two negatives make a positive.
\[\frac{12}{3}=w\]

14
Simplify  \(\frac{12}{3}\)  to  \(4\).
\[4=w\]

15
Switch sides.
\[w=4\]

Done
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