Question

check for understanding which answer choice below is equivalent to (2x + 6)4? a) 2x + 24 b) 8x + 24 c) 8x + 6 d) 32x independent practice bachelor level 1) is 4(y + 3) equivalent to 4y + 3? explain why or why not. ply the distributive property to write an equivalent expression for eac

Explanation:

Check for Understanding (Multiple Choice)

Step1: Apply Distributive Property

The distributive property states that \( a(b + c)=ab + ac \). For \( (2x + 6)4 \), we can rewrite it as \( 4(2x + 6) \). Applying the distributive property: \( 4\times2x+4\times6 \).

Step2: Calculate Each Term

Calculate \( 4\times2x = 8x \) and \( 4\times6 = 24 \). So the expression becomes \( 8x + 24 \).

To determine if \( 4(y + 3) \) is equivalent to \( 4y + 3 \), we use the distributive property. The distributive property says \( a(b + c)=ab + ac \). For \( 4(y + 3) \), applying the property gives \( 4\times y+4\times3 = 4y + 12 \). Since \( 4y + 12
eq4y + 3 \) (the constant terms \( 12\) and \( 3\) are different), they are not equivalent.

Answer:

b) \( 8x + 24 \)

Independent Practice (Question 1)