7.EE.A.1 7th Grade Expressions & Equations

Combining Like Terms & the Distributive Property

Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.

How to explain it

The anchor students hold onto: Combine like terms by adding or subtracting their coefficients; the variable part stays the same. Keep unlike terms separate, and remember that x means 1x. Distribute by multiplying the outside factor by every term inside: a(b + c) = ab + ac. A negative factor flips each sign. To factor, pull out the greatest common factor: ab + ac = a(b + c).

Combining like terms supports 7.EE.A.2 equivalent expressions and 7.EE.B.3–4 equations and inequalities — the first simplifying move on nearly every expression in Algebra 1.

Worked examples

Example 1 Same Variable

Combine: 5x + 2x.

Step 1Both terms have the variable part x.

Step 2Add the coefficients: 5 + 2 = 7.

Answer7x

Example 2 With Subtraction

Combine: 9y - 4y.

Step 1Both terms have the same variable part: y.

Step 2Subtract the coefficients: 9 - 4 = 5.

Answer5y

Example 3 With a Constant

Combine: 3x + 5 + 2x.

Step 1Like terms are 3x and 2x; the 5 is a constant.

Step 2Combine the x-terms: 3x + 2x = 5x; keep + 5.

Answer5x + 5

Common mistakes

What students write Combines unlike terms: writes 5x + 3 as 8x.

The fix Only combine same-variable terms; the 3 stays: 5x + 3.

What students write Drops the coefficient of 1: writes x + 4x as 4x.

The fix x means 1x, so x + 4x = 1x + 4x = 5x.

What students write Distributes to the first term only: 3(x + 4) = 3x + 4.

The fix Multiply the factor by EACH term: 3(x + 4) = 3x + 12.

What students write Sign error with a negative factor: -2(x - 5) = -2x - 10.

The fix A negative times a negative is positive: -2(x - 5) = -2x + 10.

Teacher tip

Head off the two predictable errors before they happen. First: Only combine same-variable terms; the 3 stays: 5x + 3. Second: x means 1x, so x + 4x = 1x + 4x = 5x.