Question

c. what is the simplified form of $5a - (2a + 3b)$?

a. $7a - 3b$
b. $3a + 3b$
c. $3a - 3b$
d. $3a - 5b$

Explanation:

Step1: Distribute the negative sign

To simplify \(5a - (2a + 3b)\), we first distribute the negative sign to the terms inside the parentheses. This means we multiply each term inside the parentheses by \(-1\). So, \(5a - (2a + 3b)=5a - 2a - 3b\).

Step2: Combine like terms

Next, we combine the like terms (the terms with \(a\)). The coefficient of \(a\) in \(5a\) is \(5\) and in \(-2a\) is \(-2\). Adding these coefficients together: \(5 - 2 = 3\). So, \(5a - 2a = 3a\). Now we have \(3a - 3b\)? Wait, no, wait. Wait, the original problem is \(5a - (2a + 3b)\). Wait, maybe I made a mistake. Wait, let's do it again.

Wait, \(5a - (2a + 3b)\) is equal to \(5a - 2a - 3b\) (because distributing the negative sign gives \(-2a - 3b\)). Then, \(5a - 2a = 3a\), so we have \(3a - 3b\)? But that's not one of the options. Wait, maybe the original problem is \(5a - (2a - 3b)\)? No, the user wrote \(5a - (2a + 3b)\). Wait, let's check the options again. The options are:

a. \(7a - 3b\)

b. \(3a + 3b\)

c. \(3a - 3b\)

d. \(3a - 6b\)

Wait, maybe I misread the problem. Wait, the user's question: "What is the simplified form of \(5a - (2a + 3b)\)?"

Wait, let's recalculate:

\(5a - (2a + 3b) = 5a - 2a - 3b = (5a - 2a) - 3b = 3a - 3b\), which is option c.

Wait, maybe I made a mistake earlier. Let's confirm:

Distribute the negative sign: \(-(2a + 3b) = -2a - 3b\)

Then, \(5a - 2a - 3b = 3a - 3b\). So the correct answer is option c.

Answer:

c. \(3a - 3b\)