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

Question

Isaiah Anthony · Accepted Answer

There are an infinite number of solutions for #x#

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 real query is: What do they mean when they say "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")#

Therefore, the number of possible solutions is infinite.

Genesis Allen · Answer

undefined To solve the equation $2 + 3x = x + 2 + 2x$, you first simplify both sides by combining like terms. Then, you isolate the variable $x$ by subtracting $x$ from both sides and subtracting 2 from both sides. Finally, you divide both sides by 2. The solution for $x$ is $x = 0$.