Question

identify the terms and like terms in the expression. (section 3.1)

1. 11x + 2x
2. 9x - 5x
3. 21x + 6 - x - 5
4. 8x + 14 - 3x + 1

Explanation:

Problem 1: \( 11x + 2x \)

Step 1: Identify Terms

Terms are the parts of the expression separated by addition or subtraction. Here, the terms are \( 11x \) and \( 2x \).

Step 2: Identify Like Terms

Like terms have the same variable (or no variable) raised to the same power. Both \( 11x \) and \( 2x \) have the variable \( x \) with exponent 1, so they are like terms.

Step 1: Identify Terms

The terms here are \( 9x \) and \( -5x \) (since subtraction is adding the opposite, so \( 9x + (-5x) \)).

Step 2: Identify Like Terms

Both \( 9x \) and \( -5x \) have the variable \( x \) with exponent 1, so they are like terms.

Step 1: Identify Terms

Rewrite the expression with addition of opposites: \( 21x + 6 + (-x) + (-5) \). The terms are \( 21x \), \( 6 \), \( -x \), \( -5 \).

Step 2: Identify Like Terms

• For \( x \)-terms: \( 21x \) and \( -x \) (both have \( x \) with exponent 1).
• For constant terms: \( 6 \) and \( -5 \) (no variable).

Answer:

Terms: \( 11x \), \( 2x \); Like Terms: \( 11x \) and \( 2x \)

Problem 2: \( 9x - 5x \)