Respuesta :

Answer:

Sometimes true.

Step-by-step explanation:

Since, an equation is true always if after solving it, we get a true statement,

It is never true if we get a false statement,

It sometimes true if we get one unique solution,

Given equation,

[tex]\frac{2}{3}x+2=2x[/tex]

[tex]\frac{2x}{3}=2x-2[/tex]

[tex]2x=6x-6[/tex]

[tex]2x-6x=-6[/tex]

[tex]-4x=-6[/tex]

[tex]\implies x = \frac{-6}{-4}=\frac{3}{2}[/tex]

Thus, the equation is true for x = 3/2.

facundo3141592

We want to see when the equation:

[tex](2/3) \cdot x + 2 = 2x[/tex]

is true.

To see this, the first thing we need to do is to isolate x in one side of the equation.

We will get:

[tex](2/3) \cdot x + 2 = 2\cdot x\\\\2 = 2\cdot x - (2/3)\cdot x\\\\2 = (2 - (2/3))\cdot x\\\\2 = (4/3)\cdot x\\\\2\cdot (3/4) = x\\\\3/2 = x[/tex]

Then we can see that the equation is only true for only one value of x, which is x = 3/2

This means that the equation is true for only one value, so we conclude that the correct option should be:

"the equation is sometimes true".

If you want to learn more, you can read:

https://brainly.com/question/1605776