An expression is shown.

Question

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