Question

Which expressions is equivalent to 7-3(2x+5)?
A. 4(2x+5)
B. 7-3(7x)
C. 7-6x+5
D. -6x-8

Answer 1

To find an expression equivalent to \( 7 - 3(2x + 5) \), we will start by distributing the \( -3 \) across the term \( (2x + 5) \):

\[
7 - 3(2x + 5) = 7 - 3 \cdot 2x - 3 \cdot 5
\]

This simplifies to:

\[
7 - 6x - 15
\]

Now, combine the constant terms:

\[
7 - 15 = -8
\]

So, we have:

\[
-6x - 8
\]

Now let's compare the simplified expression with the given options:

A. \( 4(2x + 5) \) \( \Rightarrow 8x + 20 \) (not equivalent)

B. \( 7 - 3(7x) \) \( \Rightarrow 7 - 21x \) (not equivalent)

C. \( 7 - 6x + 5 \) \( \Rightarrow 12 - 6x \) (not equivalent)

D. \( -6x - 8 \) (this is equivalent)

The correct answer is **D.** \( -6x - 8 \).