Question

1. Are equations (3x+9)=6 and x+3=2 equivalent?

2. Are expressions 3x+9 and x+3 equivalent?
3. Are equations (2) 4 and x=4(x-2) equivalent?
(x-2) and x equivalent?
X
4. Are expressions

Answer 1

1.) Yes

2.) No (unless x=-3)

3.) Yes

4.) No (unless x=3)

Explanation:

1.) 3x+9=6 is equivalent to x+3=2

`3x+9=6\\3x+9-9=6-9\\3x=-3\\(3x)/(3)=(-3)/(3)\\x=-1\\\\x+3=2\\x+3-3=2-3\\x=-1`

`3x+9=6\\3(x+3)=6\\(3(x+3))/(3)=(6)/(3)\\x+3=2`

2.) 3x+9 is not equivalent to x+3 unless x=-3

`3x+9\\3(x+3)\\eq x+3`

3.)
`(x)/((x-2))=4` is equivalent to x=4(x-2)

`(x)/((x-2))=4\\(x-2)(x)/((x-2))=4(x-2)\\x=4(x-2)\\x=4x-8\\x+8=4x-8+8\\x+8-x=4x-x\\3x=8\\x=(8)/(3)\\\\x=4(x-2)\\x=4x-8\\x+8=4x-8+8\\x+8-x=4x-x\\8=3x\\x=8/3`

`(x)/((x-2))=4\\(x-2)(x)/((x-2))=4(x-2)\\x=4(x-2)`

4.) These two expressions could only be equivalent if x=3