Academic Team Math Practice Test 2025 – The Complete All-In-One Guide to Exam Success!

Question: 1 / 400

Solve for x in the equation 3(x + 1)^(2/3) = 12.

-9, 7

To solve the equation \( 3(x + 1)^{2/3} = 12 \), we first isolate the term containing \( x \). We achieve this by dividing both sides of the equation by 3:

\[

(x + 1)^{2/3} = \frac{12}{3}

\]

\[

(x + 1)^{2/3} = 4

\]

Next, to eliminate the exponent \( \frac{2}{3} \), we raise both sides to the power of \( \frac{3}{2} \):

\[

\left((x + 1)^{2/3}\right)^{\frac{3}{2}} = 4^{\frac{3}{2}}

\]

\[

x + 1 = 4^{\frac{3}{2}}

\]

Calculating \( 4^{\frac{3}{2}} \), we first find the square root of 4, which is 2, and then raise it to the third power:

\[

4^{\frac{3}{2}} = (2^2)^{\frac{3}{2}} = 2^3 = 8

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-8, 5

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