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

1 Answer
Jan 15, 2016

Answer:

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#
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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