Learning Goal: Decide whether two expressions are equivalent by simplifying or substituting values.
Vocabulary
equivalentHaving the same value for every possible value of the variable.
substituteReplace a variable with a number to test or evaluate an expression.
simplifyRewrite an expression in its simplest equal form by combining and distributing.
like termsTerms with the same variable, which can be combined, like 2x and 6x.
What You Need to Know
Two expressions are equivalent if they simplify to the same form.
You can also test equivalence by substituting the same number into both expressions.
If even one substituted value gives different results, the expressions are NOT equivalent.
Equivalent expressions must match for ALL values, not just one lucky number.
Example: 3x + 3x = 6x, so 3x + 3x and 6x are equivalent.
x + x is 2x (not x²); adding a variable to itself doubles it.
Worked Example I Do — watch how it works
Are 2(x + 3) and 2x + 6 equivalent?
Step 1. Simplify the first: 2(x + 3) = 2x + 6 by distributing.
Step 2. Compare to the second expression: 2x + 6.
Step 3. Both simplify to 2x + 6, so they match for every value of x.
Answer: Yes, they are equivalent.
Guided Practice We Do — try it together
1. Are 4x + 2x and 6x equivalent?
💡 Hint: Combine like terms in the first expression.
2. Are 3(x + 1) and 3x + 1 equivalent?
💡 Hint: Distribute the 3 to BOTH terms inside.
3. Test x = 2: are x + 5 and 5x equivalent?
💡 Hint: Substitute 2 into each and compare.
Independent Practice You Do — show your work
1. Are 5x + x and 6x equivalent?
2. Are 2(n + 4) and 2n + 8 equivalent?
3. Are 4(y + 2) and 4y + 2 equivalent?
4. Are 7a − 3a and 4a equivalent?
5. Are x + x + x and 3x equivalent?
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.EE.A.4.
Item 1Selected Response6.EE.A.4
Which expression is equivalent to 6x + 3?
Select the correct answer.
Item 2Selected Response6.EE.A.4
Which pair of expressions is NOT equivalent?
Select the correct answer.
Item 3Constructed Response6.EE.A.4
Maya says 4(x + 1) equals 4x + 1. Is she correct? Explain.
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
Yes; 5x + x = 6x
Independent 2
Yes
Independent 3
No; 4(y + 2) = 4y + 8
Independent 4
Yes; 7a − 3a = 4a
Independent 5
Yes
Item 1 · 6.EE.A.4
A — 3(2x + 1) = 6x + 3 when distributed.
Item 2 · 6.EE.A.4
C — x + 5 adds 5 to x, but 5x multiplies x by 5; for x = 2 they give 7 and 10.
Item 3 · 6.EE.A.4
No; 4(x + 1) = 4x + 4. — The distributive property requires multiplying 4 by both x and 1, giving 4x + 4.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.EE.A.4