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 5−44(2+y)=2965-\frac{4}{4(2+y)}=\frac{29}{6}?

Let's begin!



5−44(2+y)=2965-\frac{4}{4(2+y)}=\frac{29}{6}

1
Cancel 44.
5−12+y=2965-\frac{1}{2+y}=\frac{29}{6}

2
Subtract 55 from both sides.
−12+y=296−5-\frac{1}{2+y}=\frac{29}{6}-5

3
Simplify  296−5\frac{29}{6}-5  to  −16-\frac{1}{6}.
−12+y=−16-\frac{1}{2+y}=-\frac{1}{6}

4
Multiply both sides by 2+y2+y.
−1=−16(2+y)-1=-\frac{1}{6}(2+y)

5
Simplify  16(2+y)\frac{1}{6}(2+y)  to  2+y6\frac{2+y}{6}.
−1=−2+y6-1=-\frac{2+y}{6}

6
Multiply both sides by 66.
−1×6=−2−y-1\times 6=-2-y

7
Simplify  −1×6-1\times 6  to  −6-6.
−6=−2−y-6=-2-y

8
Add 22 to both sides.
−6+2=−y-6+2=-y

9
Simplify  −6+2-6+2  to  −4-4.
−4=−y-4=-y

10
Multiply both sides by −1-1.
4=y4=y

11
Switch sides.
y=4y=4

Done
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