Problem of the Week

Updated at May 13, 2024 9:34 AM

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

How would you solve the equation \(7+4u+\frac{5}{u}=16\)?

Check out the solution below!



\[7+4u+\frac{5}{u}=16\]

1
Multiply both sides by \(u\).
\[7u+4{u}^{2}+5=16u\]

2
Move all terms to one side.
\[7u+4{u}^{2}+5-16u=0\]

3
Simplify  \(7u+4{u}^{2}+5-16u\)  to  \(-9u+4{u}^{2}+5\).
\[-9u+4{u}^{2}+5=0\]

4
Split the second term in \(-9u+4{u}^{2}+5\) into two terms.
\[4{u}^{2}-4u-5u+5=0\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[4u(u-1)-5(u-1)=0\]

6
Factor out the common term \(u-1\).
\[(u-1)(4u-5)=0\]

7
Solve for \(u\).
\[u=1,\frac{5}{4}\]

Done

Decimal Form: 1, 1.25
Cymath foriOSAndroid