Question

which expression would be added to 5x + 7 to make it equivalent to the expression 9(x + 1) (Here are the answer choices.) A. 4x - 6B. 4x + 2 C. 9x + 1 D. 14x + 8

Answer 1

Let the expression we will add be "A", thus we can write:

$5x+7+A=9(x+1)$

We can use the distributive property on the right hand side and then use a bit algebra to solve for "A". The distributive property is shown below:

$a(b+c)=ab+ac$

Let's do the algebra. The steps are shown below:

$\begin{gathered} 5x+7+A=9(x+1) \\ 5x+7+A=9x+9 \\ A=9x+9-5x-7 \\ A=4x+2 \end{gathered}$

Thus, we need to add 4x + 2 to "5x + 7" to make it equal to "9(x+1)".

The correct answer is:

B