Question

4(x + 5) + 4x + 8Which of the following is equivalent to the expressionabove?A. 4(2x + 7)B. 8(x+4)C. 5x+17D. 8x+13

Answer 1

First, let's use the distributive property to rearrange the given expression.

According to the distributive property of multiplication:

$a\cdot(b+c)=a\cdot b+a\cdot c$

Then,

$\begin{gathered} 4(x+5)+4x+8 \\ =4x+4\cdot5+4x+8 \\ =4x+20+4x+8 \end{gathered}$

Adding similar terms:

$\begin{gathered} =4x+4x+20+8 \\ =8x+28 \end{gathered}$

Now, let's compare the expression with the options.

A) 4(2x+7)

Again, using the distributive property:

$\begin{gathered} 4\cdot(2x+7) \\ =4\cdot2x+4\cdot7 \\ =8x+28 \end{gathered}$

So, the expression is equivalent to the letter A.

Let's test letter B too.

B) 8(x+4)

$\begin{gathered} 8(x+4) \\ =8\cdot x+8+4 \\ =8x+32 \end{gathered}$

The expression is not equivalent.

Also, the expression is also not equivalent to C and D.

Answer: A.