Problem of the Week

Updated at Dec 13, 2021 9:15 AM

This week's problem comes from the equation category.

How can we solve the equation \(2+3(5-\frac{5}{v})=\frac{19}{2}\)?

Let's begin!



\[2+3(5-\frac{5}{v})=\frac{19}{2}\]

1
Subtract \(2\) from both sides.
\[3(5-\frac{5}{v})=\frac{19}{2}-2\]

2
Simplify  \(\frac{19}{2}-2\)  to  \(\frac{15}{2}\).
\[3(5-\frac{5}{v})=\frac{15}{2}\]

3
Divide both sides by \(3\).
\[5-\frac{5}{v}=\frac{\frac{15}{2}}{3}\]

4
Simplify  \(\frac{\frac{15}{2}}{3}\)  to  \(\frac{15}{2\times 3}\).
\[5-\frac{5}{v}=\frac{15}{2\times 3}\]

5
Simplify  \(2\times 3\)  to  \(6\).
\[5-\frac{5}{v}=\frac{15}{6}\]

6
Simplify  \(\frac{15}{6}\)  to  \(\frac{5}{2}\).
\[5-\frac{5}{v}=\frac{5}{2}\]

7
Subtract \(5\) from both sides.
\[-\frac{5}{v}=\frac{5}{2}-5\]

8
Simplify  \(\frac{5}{2}-5\)  to  \(-\frac{5}{2}\).
\[-\frac{5}{v}=-\frac{5}{2}\]

9
Multiply both sides by \(v\).
\[-5=-\frac{5}{2}v\]

10
Simplify  \(\frac{5}{2}v\)  to  \(\frac{5v}{2}\).
\[-5=-\frac{5v}{2}\]

11
Multiply both sides by \(2\).
\[-5\times 2=-5v\]

12
Simplify  \(-5\times 2\)  to  \(-10\).
\[-10=-5v\]

13
Divide both sides by \(-5\).
\[\frac{-10}{-5}=v\]

14
Two negatives make a positive.
\[\frac{10}{5}=v\]

15
Simplify  \(\frac{10}{5}\)  to  \(2\).
\[2=v\]

16
Switch sides.
\[v=2\]

Done
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