How many solutions does the equation have?

2x + 3 = 4x + 2

Question

How many solutions does the equation have?

2x + 3 = 4x + 2

tkhunny · Answer

This called  "linear" equation.  The highest degree term is one (1).  This means it had better have no more than one (1) solution.  It may also have zero (0).

reyrey8 · Answer

so how many?

tkhunny · Answer

You tell me.  You have enough information.  0 or 1.  Those are your choices.  Prove it!

reyrey8 · Answer

no solutions, many solutions, or 1

tkhunny · Answer

We ruled out "many".  Now, prove one of the other two choices.

marypuro · Answer

you would have to sub out x and try different numbers to get x.
 so you can try 1, 2, 3
but once you try one and it doesn't work you need to try some negatives. -1,-2
when I did it I got 1/2

marypuro · Answer

so it might only have 1 solution

reyrey8 · Answer

1 solution?

reyrey8 · Answer

are u sure

tkhunny · Answer

No, it might have AT MOST one (1).  It may also have zero (0).  What is your plan to prove it?

reyrey8 · Answer

um 1 solution because its an equation? srry im not good at math

tkhunny · Answer

1) Who told you that you are not good at math?
2) Why did you believe them?

Equations can have no solution...

$x^2 = -1$

Try subtracting 2x from both sides of your equation.

reyrey8 · Answer

so the correct answer is 1 solution?

tkhunny · Answer

You tell me.  You have to PROVE it.  Did you subtract 2x from both sides?  What was the result?

reyrey8 · Answer

4x ?

tkhunny · Answer

??

2x + 3 = 4x + 2

Subtract 2x from both sides.

2x + 3 - 2x = 4x + 2 - 2x

Use the commutative Property of Addition.

2x - 2x + 3 = 4x - 2x + 2

Use the Associative Property of Addition

(2x - 2x) + 3 = (4x - 2x) + 2

Use the Substitution Principle

0 + 3 = 2x + 2

Follow the convention of failing to write zero when it doesn't help us with anything.

3 = 2x + 2

There.  Now, can we tell if there is a solution?

reyrey8 · Answer

oh so there isnt a solution

tkhunny · Answer

Have you considered subtracting 2 from each side, before deciding?

reyrey8 · Answer

i dont have time

tkhunny · Answer

Well, good luck with that.  Guessing can sometimes deliver the right answer, but there is only a little historical evidence that it leads to a valid education.