Question

jayden used the following steps to simplify the given expression.

(-3 + 2(2 + x + 3))

step 1: (= -3 + 2(x + 2 + 3))
step 2: (= -3 + 2(x + 5))
step 3: (= -3 + 2x + 10)
step 4: (= 2x + (-3) + 10)
step 5: (= 2x + 7)

what property of real numbers was used to transition from step 2 to step 3?

distributive property
associative property of addition
commutative property of addition
associative property of multiplication

Explanation:

Analyze the transition from Step 2 to Step 3

The expression in Step 2 is:

$$-3 + 2(x + 5)$$

The expression in Step 3 is:

$$-3 + 2x + 10$$

Identify the mathematical property applied

To transition from \(2(x + 5)\) to \(2x + 10\), the factor of \(2\) outside the parentheses is multiplied by each term inside the parentheses:

$$2 \cdot x + 2 \cdot 5 = 2x + 10$$

This operation represents the distributive property of multiplication over addition, commonly referred to as the distributive property.

Answer:

• distributive property (Correct answer)
• associative property of addition
• commutative property of addition
• associative property of multiplication