What “equivalent” means
Two algebraic expressions are equivalent if they give the same value for every allowed value of the variable(s). To decide this, you are not checking just one number—you are checking whether the expressions always match after simplification.
How to check
- Simplify each expression separately.
- Remove parentheses.
- Combine like terms.
- Use the order of operations carefully.
- Compare the simplified forms.
- If they become exactly the same, the expressions are equivalent.
- If they do not match, they are not equivalent.
- If needed, test a value.
- Substituting one or two convenient values can help confirm your work.
- A test is only a check; the main decision should come from simplification.
Good habits
- Keep signs attached to terms when distributing.
- Combine only like terms.
- Watch for expressions that look different but simplify to the same result.
Check your answer
After simplifying, compare the final expressions side by side. If they match exactly, your conclusion is correct. If they differ, look back for missed distribution, sign errors, or incorrect combining of terms.