To solve the expression \( 2a + 3b \) given \( a = 3 \) and \( b = -2 \):

Substitute the values of \( a \) and \( b \) into the expression:

\[
2(3) + 3(-2)
\]

Now, calculate each part:

\[
2(3) = 6
\]
\[
3(-2) = -6
\]

Add them together:

\[
6 + (-6) = 0
\]

So, the value of the expression is \( 0 \).

Would you like more details or have any questions?

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Here are 5 related questions to explore further:

1. What happens if both \( a \) and \( b \) are negative?
2. How do you factor an expression like \( 2a + 3b \)?
3. How can this expression change if \( a \) and \( b \) are functions instead of constants?
4. What is the result of \( 2a + 3b \) if \( a = -3 \) and \( b = 2 \)?
5. How does the distributive property work for expressions like this?

**Tip:** Always double-check the signs of the numbers you substitute to avoid common mistakes.

Learn how to solve the linear expression 2a + 3b by substituting a = 3 and b = -2. This problem involves basic algebra concepts, substitution, and applying the distributive property. Suitable for students in Grades 6-8.

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