Question

An expression is shown.
4 (x + 3) + 5(4x + 3)
Move all of the expressions that are equivalent to the given expression into the box.

Equivalent to 4(x + 3) +5 (4x+3)

:: 7(3x+ 2) +4x+13
:: 24x + 15
:: 3(8x + 9)
:: 24x + 27
:: 6(4x+3)+8

Answer 1

To determine which expressions are equivalent to \( 4(x + 3) + 5(4x + 3) \), we first simplify the given expression:

1. Distributing \( 4 \) in \( 4(x + 3) \):

\[
4(x + 3) = 4x + 12
\]

2. Distributing \( 5 \) in \( 5(4x + 3) \):

\[
5(4x + 3) = 20x + 15
\]

3. Combining these results:

\[
4(x + 3) + 5(4x + 3) = (4x + 12) + (20x + 15) = 24x + 27
\]

Now we will evaluate each of the given options to see which ones are equivalent to \( 24x + 27 \):

1. **Option:** \( 7(3x + 2) + 4x + 13 \)

\[
= 21x + 14 + 4x + 13 = 25x + 27 \quad \text{(not equivalent)}
\]

2. **Option:** \( 24x + 15 \)

\[
\text{(not equivalent)}
\]

3. **Option:** \( 3(8x + 9) \)

\[
= 24x + 27 \quad \text{(equivalent)}
\]

4. **Option:** \( 24x + 27 \)

\[
\text{(equivalent)}
\]

5. **Option:** \( 6(4x + 3) + 8 \)

\[
= 24x + 18 + 8 = 24x + 26 \quad \text{(not equivalent)}
\]

After checking each expression, we find that the equivalent expressions to \( 4(x + 3) + 5(4x + 3) \) are:

- \( 3(8x + 9) \)
- \( 24x + 27 \)

So, the final answers are:

- **3(8x + 9)**
- **24x + 27**