Problem of the Week

Updated at Dec 19, 2022 9:35 AM

This week's problem comes from the equation category.

How would you solve 3(5−23−v)=123(5-\frac{2}{3-v})=12?

Let's begin!



3(5−23−v)=123(5-\frac{2}{3-v})=12

1
Divide both sides by 33.
5−23−v=1235-\frac{2}{3-v}=\frac{12}{3}

2
Simplify  123\frac{12}{3}  to  44.
5−23−v=45-\frac{2}{3-v}=4

3
Subtract 55 from both sides.
−23−v=4−5-\frac{2}{3-v}=4-5

4
Simplify  4−54-5  to  −1-1.
−23−v=−1-\frac{2}{3-v}=-1

5
Multiply both sides by 3−v3-v.
−2=−3+v-2=-3+v

6
Regroup terms.
−2=v−3-2=v-3

7
Add 33 to both sides.
−2+3=v-2+3=v

8
Simplify  −2+3-2+3  to  11.
1=v1=v

9
Switch sides.
v=1v=1

Done
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