Equivalent Expressions
In short: Equivalent expressions are two written forms, like 3(x + 4) and 3x + 12, that produce the very same result whatever number replaces the variable.
6th GradeAlgebra6.EE.A.4
What is Equivalent Expressions?
Two equivalent expressions are different spellings of the same quantity. A fence can be priced as 3 sections of (x + 4) feet or as 3x feet plus 12 feet, and the final cost never changes.
Precisely, forms \(A\) and \(B\) match when every number substituted for the variable gives the same result in both. Moves that preserve the value include distributing, merging like terms, and reordering sums or products.
How to spot it
- A multiple-choice question asks which listed form matches a given one.
- You are told to simplify, expand or factor and keep the value unchanged.
- Two students write different formulas for the same perimeter or total cost.
- A table of values for two expressions is identical in every row.
The method
- Pick a legal move: distribute, combine like terms, or factor out a shared number.
- Apply it to the first expression and write the new form on the next line, one move per line so every step can be checked.
- Test the match by substituting a few values, such as 0, 1 and 5, into both versions.
- If a single value gives different results, the expressions are not equivalent.
Equivalent Expressions: solved example
Problem
Are \(2(5y – 3) + 4y\) and \(14y – 6\) equivalent? Show why.
Solution
Distribute: \(2(5y – 3) = 10y – 6\). Add the remaining \(4y\): \(10y – 6 + 4y\).
Combine like terms: \(14y – 6\). The two forms are identical, so the expressions are equivalent. Check at \(y = 2\): the left form gives \(2(7) + 8 = 22\) and the right form gives \(28 – 6 = 22\), the same value from both.
Try it
Question 1
Is \(5(n + 2)\) equivalent to \(5n + 2\)?
Show the answer
No. Distributing gives \(5n + 10\). At \(n = 1\) the first is 15 and the second is 7.
Question 2
Rewrite \(18m + 24\) as a product by pulling out the biggest shared number.
Show the answer
\(6(3m + 4)\).
Equivalent Expressions vs. Equation
Equivalent expressions agree on every input. An equation instead claims two sides are equal, and it can hold for only some inputs: \(3x + 12 = 27\) is true just when \(x = 5\).
Keep going
Lessons
Worksheets and quizzes
- Equivalent Expressions and the Distributive Property – Worksheet
- Equivalent Expressions and the Distributive Property – Quiz
- Equivalent Linear Expressions – Worksheet
- Equivalent Linear Expressions – Quiz
Related words
Whole dictionary: A–Z · 6th Grade · Algebra