please help me with is algebra 2 question.

Question

solve. Leave your answer(s) as fractions or or round two decimal places.

(3x+2) to the 2/3 power= 4

i know the answer is 2 but could it be 2 and -2. Because it is plus or minus??? please help

Answer 1

The answer is only x= 2

I will explain that for you

( 3x + 2 ) ^2/3 = 4

Raised both side to power 3

( 3x + 2 )² = 4 ³

( 3x + 2 )² = 64

Take the square root of both sides

3x + 2 = ± 8

either 3x + 2 = 8

3x = 6

x = 2

or 3 x + 2 = - 8

3x = - 10

x = - 10/ 3 neglect because it gives complex value

CHECK

for x = 2

( 3x + 2 ) ^2/3 = ( 3*2 + 2 ) ^{2/ 3} =( 6 + 2)^2/3 = (8 ) ^2/3 = ( 2³) ^2/3 = 2² = 4

for x = - 10/3

( 3x + 2 ) ^2/3 = ( 3 *( -10/3 ) + 2 )^2/3 = ( -10 + 2 ) ^2/3 = ( - 8 ) ^2/3 = ( -1 ) ^2/3 ( 8)^2/3

= 4 ( -1 ) ^2/3

this will lead us to complex value

so the only real answer is

x = 2

Answer 2

(3x + 2)^2/3 = 4

(3x + 2)² = 64

3x + 2 = ±8

3x + 2 = 8

3x = 6

x = 2

3x + 2 = -8

3x = -10

x = -10 / 3