# 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 $$2+3(5-\frac{5}{v})=\frac{19}{2}$$?

Let's begin!

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

 1 Subtract $$2$$ from both sides.$3(5-\frac{5}{v})=\frac{19}{2}-2$2 Simplify  $$\frac{19}{2}-2$$  to  $$\frac{15}{2}$$.$3(5-\frac{5}{v})=\frac{15}{2}$3 Divide both sides by $$3$$.$5-\frac{5}{v}=\frac{\frac{15}{2}}{3}$4 Simplify  $$\frac{\frac{15}{2}}{3}$$  to  $$\frac{15}{2\times 3}$$.$5-\frac{5}{v}=\frac{15}{2\times 3}$5 Simplify  $$2\times 3$$  to  $$6$$.$5-\frac{5}{v}=\frac{15}{6}$6 Simplify  $$\frac{15}{6}$$  to  $$\frac{5}{2}$$.$5-\frac{5}{v}=\frac{5}{2}$7 Subtract $$5$$ from both sides.$-\frac{5}{v}=\frac{5}{2}-5$8 Simplify  $$\frac{5}{2}-5$$  to  $$-\frac{5}{2}$$.$-\frac{5}{v}=-\frac{5}{2}$9 Multiply both sides by $$v$$.$-5=-\frac{5}{2}v$10 Simplify  $$\frac{5}{2}v$$  to  $$\frac{5v}{2}$$.$-5=-\frac{5v}{2}$11 Multiply both sides by $$2$$.$-5\times 2=-5v$12 Simplify  $$-5\times 2$$  to  $$-10$$.$-10=-5v$13 Divide both sides by $$-5$$.$\frac{-10}{-5}=v$14 Two negatives make a positive.$\frac{10}{5}=v$15 Simplify  $$\frac{10}{5}$$  to  $$2$$.$2=v$16 Switch sides.$v=2$Done v=2