Question

Absolute value inequality check

Answer 1

\[\left| x^2-2x \right|=3x-6\]

Answer 2

I got +/-3,2

Answer 3

ok so x^2-2x=3x-6
x^2-2x=-3x+6

Answer 4

so i made them quadratics and got +/-3,2

am i correct?

Answer 5

hmm i think so

Answer 6

is 2 extraneous by any chance?

Answer 7

or does it not matter if 0=0?

Answer 8

no

Answer 9

0=0 so non-extraneus

Answer 10

extraneous is just when the values don't equal each other right?

Answer 11

\[|x^2-2x|=3x-6\]
To check you solutions, plug them into the original equation

The first solution you got was x=3
\[|(3)^2-2(3)|=3(3)-6\\
|9-6|=9-6\\
|3|=3\\
3=3\]
Which is always true, so x=3 is a solution.

The second solution you got was x=-3
\[|(-3)^2-2(-3)|=3(-3)-6\\
|9+6|=-9-6\\
|15|=-15\\
15=-15\]
Which is never true, so x=-3 is not a solution (check your working)

The third solution you got was x=2
\[|(2)^2-2(2)|=3(2)-6\\
|4-4|=6-6\\|0|=0\\
0=0\]
Which is always true so x=2 is a solution.

Answer 12

Oh, i see

Answer 13

Is the equation meant to be an in-equation?

Answer 14

not sure what that means

Answer 15

The question in the original post says
"Absolute value INEQUALITY check"

an inequality has an inequality sign (such as \(<,>\leq,\geq\))

whereas; a equation has an equality sign \(=\)