Problem of the Week

Updated at Oct 12, 2020 10:33 AM

This week we have another equation problem:

How can we solve the equation 6(44v)2=326{(\frac{4}{4v})}^{2}=\frac{3}{2}?

Let's start!



6(44v)2=326{(\frac{4}{4v})}^{2}=\frac{3}{2}

1
Cancel 44.
6(1v)2=326{(\frac{1}{v})}^{2}=\frac{3}{2}

2
Use Division Distributive Property: (xy)a=xaya{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}.
6×1v2=326\times \frac{1}{{v}^{2}}=\frac{3}{2}

3
Simplify  6×1v26\times \frac{1}{{v}^{2}}  to  6v2\frac{6}{{v}^{2}}.
6v2=32\frac{6}{{v}^{2}}=\frac{3}{2}

4
Multiply both sides by v2{v}^{2}.
6=32v26=\frac{3}{2}{v}^{2}

5
Simplify  32v2\frac{3}{2}{v}^{2}  to  3v22\frac{3{v}^{2}}{2}.
6=3v226=\frac{3{v}^{2}}{2}

6
Multiply both sides by 22.
6×2=3v26\times 2=3{v}^{2}

7
Simplify  6×26\times 2  to  1212.
12=3v212=3{v}^{2}

8
Divide both sides by 33.
123=v2\frac{12}{3}={v}^{2}

9
Simplify  123\frac{12}{3}  to  44.
4=v24={v}^{2}

10
Take the square root of both sides.
±4=v\pm \sqrt{4}=v

11
Since 2×2=42\times 2=4, the square root of 44 is 22.
±2=v\pm 2=v

12
Switch sides.
v=±2v=\pm 2

Done
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