Problem of the Week

Updated at Aug 2, 2021 1:21 PM

For this week we've brought you this equation problem.

How can we solve the equation 4(v−3)(v−3)5=45\frac{4(v-3)(v-3)}{5}=\frac{4}{5}?

Here are the steps:



4(v−3)(v−3)5=45\frac{4(v-3)(v-3)}{5}=\frac{4}{5}

1
Use Product Rule: xaxb=xa+b{x}^{a}{x}^{b}={x}^{a+b}.
4(v−3)25=45\frac{4{(v-3)}^{2}}{5}=\frac{4}{5}

2
Multiply both sides by 55.
4(v−3)2=45×54{(v-3)}^{2}=\frac{4}{5}\times 5

3
Cancel 55.
4(v−3)2=44{(v-3)}^{2}=4

4
Divide both sides by 44.
(v−3)2=1{(v-3)}^{2}=1

5
Take the square root of both sides.
v−3=±1v-3=\pm \sqrt{1}

6
Simplify  1\sqrt{1}  to  11.
v−3=±1v-3=\pm 1

7
Break down the problem into these 2 equations.
v−3=1v-3=1
v−3=−1v-3=-1

8
Solve the 1st equation: v−3=1v-3=1.
v=4v=4

9
Solve the 2nd equation: v−3=−1v-3=-1.
v=2v=2

10
Collect all solutions.
v=4,2v=4,2

Done
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