Question

Which expression is equivalent to 5(3x + 9)?
9
a) 5x+$65=$240; x=$35
b) 5x-$65=$240; x=$61
c) $65-5x=$240; x=-$35
d) 5x+$240=$65; x=$45

Answer 1

To find an equivalent expression to \( 5(3x + 9) \), we'll start by simplifying it:

\[
5(3x + 9) = 5 \cdot 3x + 5 \cdot 9 = 15x + 45
\]

Next, let's see if any of the given options can be manipulated to yield that expression.

1. a) \( 5x + 65 = 240 \)
- Solve for \( x \):
\[
5x = 240 - 65
\]
\[
5x = 175 \quad \Rightarrow \quad x = 35
\]
- This does not match \( 15x + 45 \).

2. b) \( 5x - 65 = 240 \)
- Solve for \( x \):
\[
5x = 240 + 65 = 305 \quad \Rightarrow \quad x = 61
\]
- This does not match \( 15x + 45 \).

3. c) \( 65 - 5x = 240 \)
- Solve for \( x \):
\[
-5x = 240 - 65 \quad \Rightarrow \quad -5x = 175 \quad \Rightarrow \quad x = -35
\]
- This does not match \( 15x + 45 \).

4. d) \( 5x + 240 = 65 \)
- Solve for \( x \):
\[
5x = 65 - 240 \quad \Rightarrow \quad 5x = -175 \quad \Rightarrow \quad x = -35
\]
- This does not match \( 15x + 45 \).

None of the options a), b), c), or d) provide an equivalent expression to \( 15x + 45 \).

Thus, we need to find a connection between these expressions and the simplified form \( 15x + 45 \).

None of the equations in the current options are equivalent to \( 5(3x + 9) \). Therefore, **there is no option that is equivalent to \( 5(3x + 9) \)** from the choices given.

If we consider \( 15x + 45 \) as a function of \( x \), we can see each option produces a specific value of \( x \), but does not yield \( 15x + 45 \) inherently.

In conclusion, the mathematically equivalent form of \( 5(3x + 9) \) is \( 15x + 45 \), and none of the provided options represent this equivalence.