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:

Step1: Analyze Step 2 to Step 3

Step 2: \(-3 + 2(x + 5)\)
Step 3: \(-3 + 2x + 10\)
We use the distributive property here, which states that \(a(b + c)=ab+ac\). Applying this to \(2(x + 5)\), we get \(2\times x+2\times5 = 2x + 10\).

Step2: Confirm the Property

The transition from Step 2 to Step 3 is achieved by applying the distributive property, as we distributed the 2 across the terms inside the parentheses.

Answer:

distributive property