Simplify; 3x - (p - x) - (r - p)

Analyze the question: We need to remove the brackets carefully and then collect like terms. The key point is that a minus sign in front of a bracket changes the sign of every term inside it.

Concept: −(a − b) = −a + b

Solution:

3x − (p − x) − (r − p)

Step 1: Expand the first bracket: −(p − x) = −p + x

Step 2: Expand the second bracket: −(r − p) = −r + p

Step 3: Put everything together: 3x − p + x − r + p

Step 4: Collect like terms:

• x terms: 3x + x = 4x
• p terms: −p + p = 0
• r term: −r

Result: 4x − r

Tip: When you see a minus sign before a bracket, flip the sign of every term inside it. Most mistakes in this type of question come from forgetting to change the sign of the second term in the bracket. Also, look for terms that cancel (like −p and +p here) because they often signal you are on the right track.