Pre-Algebra
Expressions and equations
Equivalent expressions and properties of operations
20 practice questions
0 video lessons
Theory + worked examples
Equivalent Expressions and Properties of Operations
Texas Pre-Algebra (TEKS) • Standard 6.7(D) • Expressions & Equations
Equivalent Expressions and Properties of Operations is a topic in Expressions & Equations in the Texas Essential Knowledge and Skills. It is aligned to Standard 6.7(D), which requires students to generate equivalent expressions using the properties of operations.
Equivalent expressions have the same value for every input; the properties of operations let you rewrite one as another.
Theory
Equivalent expressions have the same value for every value of the variable.
Use the commutative, associative, and distributive properties, and combine like terms, to rewrite them.
The properties of operations.
Equivalent expressions.
The distributive property:
\[a(b+c)=ab+ac\]
Like terms have the same variable part.
How to simplify to an equivalent expression
- Distribute across parentheses.
- Identify like terms.
- Add or subtract their coefficients.
- Write the simplified form.
Example 1 — Distribute
Expand \(4(x+3)\).
Solution
Distribute the \(4\).
| \(4(x+3)\) | \(=\) | \(4x+12\) |
Example 2 — Combine like terms
Simplify \(5x+2x\).
Solution
Add the coefficients.
| \(5x+2x\) | \(=\) | \(7x\) |
Example 3 — Both
Simplify \(2(x+4)+3x\).
Solution
Distribute, then combine.
| \(2x+8+3x\) | \(=\) | \(5x+8\) |
Example 4 — Factor
Write \(6x+9\) as a product.
Solution
Factor out \(3\).
| \(6x+9\) | \(=\) | \(3(2x+3)\) |
Common pitfalls
Distribute to every term inside the parentheses.
Only combine like terms — \(x\) and \(x^2\) differ.
Keep the variable when adding like terms.
Frequently asked questions
What are equivalent expressions?
Expressions with the same value for every input.
What is the distributive property?
\(a(b+c)=ab+ac\).
What are like terms?
Terms with the same variable part.
Expand \(4(x+3)\).
\(4x+12\).
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