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

Jan 15, 2016

There are an infinite number of solutions for $x$

#### Explanation:

Given: $\textcolor{b r o w n}{2 + 3 x = x + 2 + 2 x}$

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 $\textcolor{b l u e}{3 x}$ 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!!!!
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Assumption}}$

$\textcolor{b r o w n}{\text{Asking: for what values of "x" is the equation true?}}$

$\textcolor{g r e e n}{x \text{ may assume any value and in each case the equation is true}}$

Thus there are an infinite number of solutions