Question

Solve |2y - 2| = y.

Answer 1

The left side of the equation can only be 0 or positive. Since\[2y-2=0\]when \[y=1\]we shall restrict the domain of y to\[D=[1,\infty)\]This reduces the original equation to\[2y-2=y\]Then we can solve it easily.\[y-2=0\]\[y=2\]

Answer 2

so is y after the equation sign 1?

Answer 3

No. y=1 is the point at which the left side is no longer negative. Restricting the domain to [1,Infinity) allows us to remove the absolute value signs from the left side of the equation.

Answer 4

okay

Answer 5

hmm careful here

Answer 6

evidently if there is to be a solution it must be the case that \(y\geq 0\) since the absolute value cannot be negative, but it does not follow that \(y>1\)

Answer 7

True, there is another solution I didn't think about, for \[2-2y=y\]in the domain of [0,1)

Answer 8

you still need to break in to two parts, \(2y-2<0\) or \(y<1\) \if \(y<1\) then \(|2y-2|=2-2y\) and you need to solve \(2-2y=y\)

Answer 9

which only takes two steps
\[2-2y=y\]
\[2=3y\]
\[\frac{2}{3}=y\] which works as well

Answer 10

2/3, 2
2, 3
2, 5
1/3, 2

I dont get the fraction part of it?