# Problem of the Week

## Updated at Aug 20, 2018 4:47 PM

How would you solve $$\frac{{(\frac{v+2}{3})}^{2}}{6}=\frac{2}{3}$$?

Below is the solution.

$\frac{{(\frac{v+2}{3})}^{2}}{6}=\frac{2}{3}$

 1 Use Division Distributive Property: $${(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}$$.$\frac{\frac{{(v+2)}^{2}}{{3}^{2}}}{6}=\frac{2}{3}$2 Simplify  $${3}^{2}$$  to  $$9$$.$\frac{\frac{{(v+2)}^{2}}{9}}{6}=\frac{2}{3}$3 Simplify  $$\frac{\frac{{(v+2)}^{2}}{9}}{6}$$  to  $$\frac{{(v+2)}^{2}}{9\times 6}$$.$\frac{{(v+2)}^{2}}{9\times 6}=\frac{2}{3}$4 Simplify  $$9\times 6$$  to  $$54$$.$\frac{{(v+2)}^{2}}{54}=\frac{2}{3}$5 Multiply both sides by $$54$$.${(v+2)}^{2}=\frac{2}{3}\times 54$6 Use this rule: $$\frac{a}{b} \times c=\frac{ac}{b}$$.${(v+2)}^{2}=\frac{2\times 54}{3}$7 Simplify  $$2\times 54$$  to  $$108$$.${(v+2)}^{2}=\frac{108}{3}$8 Simplify  $$\frac{108}{3}$$  to  $$36$$.${(v+2)}^{2}=36$9 Take the square root of both sides.$v+2=\pm \sqrt{36}$10 Since $$6\times 6=36$$, the square root of $$36$$ is $$6$$.$v+2=\pm 6$11 Break down the problem into these 2 equations.$v+2=6$$v+2=-6$12 Solve the 1st equation: $$v+2=6$$.1 Subtract $$2$$ from both sides.$v=6-2$2 Simplify  $$6-2$$  to  $$4$$.$v=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$v=4$13 Solve the 2nd equation: $$v+2=-6$$.1 Subtract $$2$$ from both sides.$v=-6-2$2 Simplify  $$-6-2$$  to  $$-8$$.$v=-8$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$v=-8$14 Collect all solutions.$v=4,-8$Done v=4,-8