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(5−5v)=1922+3(5-\frac{5}{v})=\frac{19}{2}?

Let's begin!



2+3(5−5v)=1922+3(5-\frac{5}{v})=\frac{19}{2}

1
Subtract 22 from both sides.
3(5−5v)=192−23(5-\frac{5}{v})=\frac{19}{2}-2

2
Simplify  192−2\frac{19}{2}-2  to  152\frac{15}{2}.
3(5−5v)=1523(5-\frac{5}{v})=\frac{15}{2}

3
Divide both sides by 33.
5−5v=15235-\frac{5}{v}=\frac{\frac{15}{2}}{3}

4
Simplify  1523\frac{\frac{15}{2}}{3}  to  152×3\frac{15}{2\times 3}.
5−5v=152×35-\frac{5}{v}=\frac{15}{2\times 3}

5
Simplify  2×32\times 3  to  66.
5−5v=1565-\frac{5}{v}=\frac{15}{6}

6
Simplify  156\frac{15}{6}  to  52\frac{5}{2}.
5−5v=525-\frac{5}{v}=\frac{5}{2}

7
Subtract 55 from both sides.
−5v=52−5-\frac{5}{v}=\frac{5}{2}-5

8
Simplify  52−5\frac{5}{2}-5  to  −52-\frac{5}{2}.
−5v=−52-\frac{5}{v}=-\frac{5}{2}

9
Multiply both sides by vv.
−5=−52v-5=-\frac{5}{2}v

10
Simplify  52v\frac{5}{2}v  to  5v2\frac{5v}{2}.
−5=−5v2-5=-\frac{5v}{2}

11
Multiply both sides by 22.
−5×2=−5v-5\times 2=-5v

12
Simplify  −5×2-5\times 2  to  −10-10.
−10=−5v-10=-5v

13
Divide both sides by −5-5.
−10−5=v\frac{-10}{-5}=v

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

15
Simplify  105\frac{10}{5}  to  22.
2=v2=v

16
Switch sides.
v=2v=2

Done
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