Question

WILL GIVE MEDAL AND FAN!!!!

Debbie and Trisha are looking at the equation the square root of the quantity of 4 times x minus 6 equals square root of x . Debbie says that the solution is extraneous. Trisha says that the solution is non-extraneous. Is Debbie correct? Is Trisha correct? Are they both correct? Justify your response by solving this equation, explaining each step with complete sentences.

Answer 1

ok lets write equation on left hand side
square root of the quantity of 4 times x minus 6
first write without squareroot
4 times x= 4x and subtract 6 now .....so
is 4x-6
now take square root
4x−6−−−−−√

Answer 2

x=2

Answer 3

they cant be both correct

Answer 4

now you do the rest

Answer 5

Okay I'm super confused o_o

Answer 6

@Flightmaster201

Answer 7

hey write the equation in numeric form u will understand all

Answer 8

I'm just really bad at this. It would help if you like walked me through it and tried to teach me.

Answer 9

ok

Answer 10

4 times x means
4 *x
which can be wrtten as
4x

Answer 11

squate root 4 times x minus 6
means
sqrt 4x -6

Answer 12

okayy I get that part.

Answer 13

squate root 4 times x minus 6 equalls sqrt x
means
sqrt 4x -6 = sqrt x
this is the equation given in the qustion

Answer 14

get it

Answer 15

now take squares both sides in order to eliminate the sqrt
then the equation will become
4x -6 =x
4x = x + 6
4x - x = 6
3x = 6
divide both sides by 3
x = 2
so
which is not extranous roots

Answer 16

debbie is wrong
which means they both r wrong
then trisha is right