Question
What's the first step when solving (x-3)2/5=20
Multiply both sides by 5
Dived both sides by 5
Subtract both sides by 5
Add3 to both sudes
Multiply both sides by 5
Dived both sides by 5
Subtract both sides by 5
Add3 to both sudes
Answers
GPT-4o mini
To solve the equation \((x - 3)^{2/5} = 20\), the first step is to eliminate the exponent on the left side. You can do this by raising both sides to the power of \(\frac{5}{2}\):
\[
((x - 3)^{2/5})^{\frac{5}{2}} = 20^{\frac{5}{2}}
\]
This simplifies the left side to \(x - 3\):
\[
x - 3 = 20^{\frac{5}{2}}
\]
You would then proceed to isolate \(x\) by adding 3 to both sides:
\[
x = 20^{\frac{5}{2}} + 3
\]
So, none of the options you provided (Multiply both sides by 5, Divide both sides by 5, Subtract both sides by 5, Add 3 to both sides) are the correct first step. The first step is to raise both sides to the power of \(\frac{5}{2}\).
\[
((x - 3)^{2/5})^{\frac{5}{2}} = 20^{\frac{5}{2}}
\]
This simplifies the left side to \(x - 3\):
\[
x - 3 = 20^{\frac{5}{2}}
\]
You would then proceed to isolate \(x\) by adding 3 to both sides:
\[
x = 20^{\frac{5}{2}} + 3
\]
So, none of the options you provided (Multiply both sides by 5, Divide both sides by 5, Subtract both sides by 5, Add 3 to both sides) are the correct first step. The first step is to raise both sides to the power of \(\frac{5}{2}\).