If 1/2 the result obtained when 2 is subtracted from 5x is equal to th

Hello sony1000

You translated the question incorrectly and thus, confused yourself.
We shall discuss both, your translation as well as the correct translation, of this statement.

YOUR TRANSLATION
There are two big mistakes that you made. We will go over them one by one:
Question says: “If 1/2 the result obtained when 2 is subtracted from 5x is equal to the sum of 10 and 3x, what is the value of x?”

ONE: You translated the statement into the following mathematical equation:

• ½ = 5x – 2

This equation conveys that “1/2 IS the result when 2 is subtracted from 5x”.
Notice the highlighted “is”. I agree that “is” translates to the equal to (=) sign, but we do NOT have an “is” in the question!

TWO: Now, that’s not all that you did wrong. You completely missed the rest of the statement - “is equal to the sum of 10 and 3x”

Let’s now correct the errors you made and look at the correct translation.

CORRECT TRANSLATION

ONE: In the statement “If 1/2 the result obtained when 2 is subtracted from 5x”
Replace ½ with its English translation “half”. So, the statement becomes:

• “If half the result obtained when 2 is subtracted from 5x.”
  
  • “Half the result” means that the result, that is (5x – 2), is halved .
  • Now, half of (5x – 2) = ½ × (5x – 2) = (5x – 2)/2

Go through the following examples to understand this better. Say, I denote the numbers of pens I have by ‘x’. Then:
- “Half the number of pens” is half of x or half times x, that is, x/2.
- “Twice the number of pens” is 2 times x, that is, 2x.
- “Three times the number of pens” is 3 times x, that is, 3x.
It’s just multiplication!

TWO: The remainder of the statement says - “…. is equal to the sum of 10 and 3x”.
o So, the expression obtained through translation part-1 is equal to 10 + 3x (sum of 10 and 3x).

Combing both parts, we have: \(\frac{(5x – 2)}{2}\) = 10 + 3x
And that’s it! This is the correct translation of the question statement.

You see how such a small translation can cause a question to be incorrect. Be super careful!

Hope this helps!

Best Regards,
Ashish Arora
Quant Expert, e-GMAT