Question

How do you solve `2 + 3x = x + 2 + 2x`?

Answer 1

There are an infinite number of solutions for `x`

Explanation:

Given: `color(brown)(2+3x=x+2+2x)`

Grouping like terms:
`color(brown)(2+3x=2+(x+2x)`

Adding all the x's that are on the same side:
`color(brown)(2+3x=2+3x`

Subtract `color(blue)(3x)` from both sides

`color(brown)((2+3x)color(blue)(-3x) =(2+3x)color(blue)(-3x)`

`2=2`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I have came across this type of problem yesterday:

The question really is: What do they mean by 'solve'

After discussion with others it was decided that they are after all the values of `x` for which this equation is true. Perhaps a different wording of the question would be more appropriate!!!!
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Assumption")`

`color(brown)("Asking: for what values of "x" is the equation true?")`

`color(green)(x" may assume any value and in each case the equation is true")`

Thus there are an infinite number of solutions