Identify When Two Expressions Are Equivalent

For each pair of expressions: first test with substitution, then verify or disprove algebraically.

Grade 6·19 problems·~25 min·Common Core Math - Grade 6·standard·6-ee-a-4

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If $x = 3$ , which expression has a value of 12?

$x + 12$

$3x + 3$

$2x + 4$

$4x + 1$

What does it mean for two expressions to be equivalent?

They look the same when written.

They give the same result for one specific value.

They give the same result for every value substituted.

They have the same number of terms.

Use the distributive property to expand $2(n + 3)$ .

$2n + 3$

$n + 6$

$2n + 6$

$2n + 5$

Test $y = 5$ : are $y + y + y$ and $3y$ equivalent when $y = 5$ ?

No — they give different results.

Yes — $y + y + y = 15$ and $3y = 15$ , so they match at $y = 5$ .

Cannot be determined from one test.

Yes — because both expressions have $y$ in them.

Test whether $5n + 3$ and $5(n + 3)$ are equivalent by substituting $n = 1$ .

Both equal 8 at $n = 1$ , so they might be equivalent.

Both equal 20 at $n = 1$ , so they are equivalent.

$5(1) + 3 = 8$ and $5(1 + 3) = 20$ . They differ, so the expressions are NOT equivalent.

They are equivalent because both contain 5 and 3.

A student claims $3(x + 2)$ and $3x + 2$ are equivalent because '3 times $x$ plus 2 is the same either way.' Is the student correct?

Yes — both expressions have 3, $x$ , and 2.

Yes — $3(x + 2) = 3x + 2$ by the distributive property.

No — $3(x + 2) = 3x + 6$ by the distributive property. $3x + 2 \neq 3x + 6$ .

Cannot be determined without knowing the value of $x$ .

Simplify $4(2x + 1)$ to confirm whether it is equivalent to $8x + 4$ .

Enter 1 if equivalent, 0 if not equivalent.

Which pair of expressions IS equivalent?

$4y + 2$ and $2(2y + 2)$

$3a + 6$ and $3(a + 2)$

$2x + 4$ and $2(x + 4)$

$5n + 3$ and $5(n + 3)$

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