Problem of the Week

Updated at Mar 18, 2019 5:40 PM

This week's problem comes from the equation category.

How would you solve the equation \(5-\frac{4}{4(2+y)}=\frac{29}{6}\)?

Let's begin!



\[5-\frac{4}{4(2+y)}=\frac{29}{6}\]

1
Cancel \(4\).
\[5-\frac{1}{2+y}=\frac{29}{6}\]

2
Subtract \(5\) from both sides.
\[-\frac{1}{2+y}=\frac{29}{6}-5\]

3
Simplify  \(\frac{29}{6}-5\)  to  \(-\frac{1}{6}\).
\[-\frac{1}{2+y}=-\frac{1}{6}\]

4
Multiply both sides by \(2+y\).
\[-1=-\frac{1}{6}(2+y)\]

5
Simplify  \(\frac{1}{6}(2+y)\)  to  \(\frac{2+y}{6}\).
\[-1=-\frac{2+y}{6}\]

6
Multiply both sides by \(6\).
\[-1\times 6=-2-y\]

7
Simplify  \(-1\times 6\)  to  \(-6\).
\[-6=-2-y\]

8
Add \(2\) to both sides.
\[-6+2=-y\]

9
Simplify  \(-6+2\)  to  \(-4\).
\[-4=-y\]

10
Multiply both sides by \(-1\).
\[4=y\]

11
Switch sides.
\[y=4\]

Done
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