Simplify: 3(x + 5) - 3/2x - 9
Show algebraic work: __________________________________
CCSS 7.EE.A.1 · add, subtract & simplify expressions
Simplifying Linear Expressions Worksheet Generator
Practice the actual 7.EE.A.1 chain: distribute across parentheses, preserve signs, then combine like terms into an equivalent linear expression. Standard and challenge sets introduce exact rational coefficients without turning the worksheet into an eighth-grade equation set.
Live worksheet preview
Simplify Linear Expressions
Simplify linear expressions · Grade 7 standard · Seed 271801
1.
2.
Simplify: -3/2(x - 5/2) - 5x + 3/2
Show algebraic work: __________________________________
3.
Simplify: -5/2(x - 3) - 3/2x - 7/2
Show algebraic work: __________________________________
4.
Simplify: 2(x - 12) + 6x + 10
Show algebraic work: __________________________________
5.
Simplify: 2(x - 7/2) + 6x + 4
Show algebraic work: __________________________________
6.
Simplify: 2(x + 9) - 1/2x - 3
Show algebraic work: __________________________________
7.
Simplify: -5/2(x - 2) + 5x - 6
Show algebraic work: __________________________________
8.
Simplify: 1/2(x + 3) + x - 7
Show algebraic work: __________________________________
9.
Simplify: -4(x + 8) + 5/2x + 1/2
Show algebraic work: __________________________________
10.
Simplify: 4(x + 5) + 1/2x + 3
Show algebraic work: __________________________________
Construction rule: equations are built around known exact solutions, expression rewrites use exact rational arithmetic, 7.EE.3 money stays in integer cents, and inequality answer graphs are withheld until answers are revealed.
Simplifying a linear expression by combining like terms
Like terms have the same variable part, so 3x and 2x can be combined, but 3x and 5 cannot. To simplify, first distribute any number outside parentheses, then add or subtract the like terms, keeping the sign in front of each term. The result is an equivalent expression with fewer terms.
Worked examples
- 3x + 5 + 2x − 1: combine 3x + 2x = 5x and 5 − 1 = 4, so the result is 5x + 4.
- 2(x + 3) + 4x: distribute to get 2x + 6 + 4x, then combine 2x + 4x = 6x. The result is 6x + 6.
- 7x − 3 − 4x + 8: the x terms give 7x − 4x = 3x and the numbers give −3 + 8 = 5, so 3x + 5.
Common slips
- Combining unlike terms. 3x + 5 is not 8x.
- Dropping a negative sign. In 7x − 3 − 4x + 8, the −3 stays negative when the terms are combined.
- Distributing to only the first term. 2(x + 3) is 2x + 6, not 2x + 3.
How to use this worksheet
Ask students to circle the like terms in matching colors before combining. The answer key shows the simplified expression, so students can compare the number of terms and the signs.
Common Core connection
- 7.EE.A.1 · Apply properties of operations to add, subtract, factor, and expand linear expressions.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Classroom note 1
Distribute before combining terms that are not yet like terms.
Classroom note 2
A negative factor changes the sign of every term inside the parentheses.
Classroom note 3
The expression -(x - 4) means -1(x - 4) and becomes -x + 4; writing -x - 4 is the classic sign error.
Classroom note 4
Only combine terms with an identical variable part: 3x and 5x combine, but 3x and 3x squared do not.
Classroom note 5
Keep fractional coefficients exact; do not replace them with rounded decimals midway through the rewrite.
Continue the 7.EE progression
Move to another Grade 7 algebra skill
Questions people ask
Do these include rational coefficients?
Yes. Foundation mode is mostly integer-based; standard and challenge modes introduce exact fractional coefficients.
Are students solving for x?
No. This route is expression rewriting, not equation solving; solving appears later in the 7.EE progression.
What counts as simplest form on the answer key?
One term for each distinct variable part plus at most one constant, with every set of parentheses resolved. 2x + 3x + 5 is not finished; 5x + 5 is.
Is 'combine like terms' the same as 'simplify'?
Combining like terms is the last step of simplifying. Under 7.EE.A.1 students first distribute to clear parentheses, then combine, so a full simplification usually needs both moves.