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Using both the Commutative and Associative Properties, determine whether the following two expressions are equivalent:

Expression #1: (2x+4)−2+3x
(
2
𝑥
+
4
)
−
2
+
3
𝑥
Expression #2: 5x+2
5
𝑥
+
2


(1 point)
Responses

The expressions are equivalent.
The expressions are equivalent.

The expressions are NOT equivalent.

1 answer

To determine whether the two expressions are equivalent, let's simplify Expression #1 step-by-step:

Expression #1: \( (2x + 4) - 2 + 3x \)

  1. First, simplify \( (2x + 4) - 2 \): \[ 2x + 4 - 2 = 2x + 2 \]

  2. Now, add \( 3x \) to \( 2x + 2 \): \[ 2x + 2 + 3x = (2x + 3x) + 2 = 5x + 2 \]

Now we have simplified Expression #1 to \( 5x + 2 \).

Now let's compare it to Expression #2:

Expression #2: \( 5x + 2 \)

Both Expression #1 and Expression #2 simplify to \( 5x + 2 \).

Since both expressions are equal, we can conclude that:

The expressions are equivalent.