What must be added to (2x - 3y) to get (x - 2y)?

Analyze the question: We need an expression that, when added to (2x − 3y), gives (x − 2y).

Concept: If a + ? = b, then ? = b − a.

Solution:

Let the expression to be added be E.

(2x − 3y) + E = x − 2y

E = (x − 2y) − (2x − 3y)

Remove the brackets carefully, changing the signs in the second bracket:

E = x − 2y − 2x + 3y

Collect like terms:

• x terms: x − 2x = −x
• y terms: −2y + 3y = y

E = −x + y = y − x

Check: (2x − 3y) + (y − x) = x − 2y ✓

Answer: Option B (y − x).

Tip: For "what must be added to A to get B", always compute B − A (target minus starting value). Be careful with the negative sign in front of the bracket, because it changes the sign of every term inside. (Note that option C is probably a misprint, since "x − 5x" would simplify to −4x, which does not work.)