solve and check for extraneous solutions

Tutors, sign in to answer this question.

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

[( 2X + 12) ^2] / 3 - 3 = 13

( 2X +12) ^2 = 48

( 2X +1 2 ) ^2 - 48 =0

( 2X +12 + 4 √3 ) ( 2X +12 - 4 √3 ) =0

X = -12 -4√3 X = -12+4√3

2 2

X = - 6 ± 2 √3

(2x + 12)^(2/3) - 3 = 13 [add 3]

(2x + 12)^(2/3) = 16 [exponentiate by 3/2]

2x + 12 = 16^(3/2) [simplify]

2x + 12 = 64 [subtract 12]

2x = 52 [divide by 2]

x = 26

Now check to make sure the answer is not extraneous.

(2(26) + 12)^(2/3) - 3 = 13

(2(26) + 12)^(2/3) - 3 = 13

(52 + 12)^(2/3) - 3 = 13

64^(2/3) - 3 = 13

16 - 3 = 13

13 = 13

((2x+12)^2)/3=16

(2x+12)^2=16*3

|2x+12|=4*sqrt(3)

2x+12=±4*sqrt(3)

x+6=±2*sqrt(3)

x=-6±2*sqrt(3)

B. ((2x+12)^(2/3))-3=13

((2x+12)^2)^(1/3))=16

(2x+12)^2=16^3

|2x+12|=16^(3/2)=64

2x+12=±64

x+6=±32

x=-6±32=-38 or 24

C. (2x+12)^((2/3)-3)=13

(2x+12)^(-7/3)=13

Raise both sides to -3/7 power:

(2x+12)=13^(-3/7)

2x=13^(-3/7)-12

x=(13^(-3/7))/2-6

x≈ -5.83344191822469

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Randee S.

Dynamic, versatile tutor for core subject areas K-12

$8.75 per 15 min

View Profile >

Laura M.

Graduate Student Experienced in Tutoring Variety of Subjects

$11.25 per 15 min

View Profile >

Devin M.

Experienced and Enthusiastic Math Tutor!

$10 per 15 min

View Profile >

## Comments