6C Equivalent Expressions Study Guide

Key Vocabulary

Equivalent Expressions — two expressions that have the same value for every number you substitute. (expresiones equivalentes)

Like Terms — terms that have the same variable raised to the same power (e.g., 3x and 5x). (términos semejantes)

Combine — to add or subtract like terms to make a simpler expression. (combinar)

Simplify — to rewrite an expression in its shortest, simplest form. (simplificar)

Visual Example — What Are Like Terms?

Like terms have the SAME variable part:

3x and 5x → LIKE (both have x)
4y and 2y → LIKE (both have y)
7 and 3 → LIKE (both are constants — no variable)

3x and 4y → NOT like (different variables)

Combining like terms:
3x + 5x + 2 + 7
= (3x + 5x) + (2 + 7)
= 8x + 9

Step-by-Step

1 Identify like terms. Group terms with the same variable together.
2 Combine the coefficients (add or subtract the numbers in front of the variable).
3 Combine constants (numbers without variables) together.
4 Write the simplified expression.

Example: Simplify 4x + 3 + 2x − 1
Group like terms: (4x + 2x) + (3 − 1)
Combine: 6x + 2
Answer: 6x + 2

Formula Box

Like terms: same variable, same exponent
Combine by adding/subtracting coefficients

To check equivalence: substitute the same value into both expressions — they should give the same result.

Watch Out!

3x + 2y does NOT equal 5xy! You can only combine terms with the SAME variable.
x and x² are NOT like terms. The exponents must match too.
Keep the sign with the term. In 5x − 3x, the −3x means you subtract: 5x − 3x = 2x.
Constants are like terms with each other. 4 + 7 = 11 (combine them).

Practice Problems

1. Simplify: 7x + 3x

2. Simplify: 5n + 4 + 2n + 6

3. Simplify: 9x − 3x + 2