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: $7(3x+2)+4x+13$

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

2. Option: $24x+15$

   $$\text{(not equivalent)}$$

3. Option: $3(8x+9)$

   $$=24x+27\text{(equivalent)}$$

4. Option: $24x+27$

   $$\text{(equivalent)}$$

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

   $$=24x+18+8=24x+26\text{(not equivalent)}$$

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