Respuesta :
The expressions we have are:
[tex]\begin{gathered} 2x+24\text{ and }2(x+4) \\ 9+3x\text{ and }3(3+x) \\ 4(x-1)\text{ and }4x-14 \\ 5(2x-1)\text{ and }5x-5 \end{gathered}[/tex]To find the correct answer, we have to use the distributive property on the options and check if the expressions are the same.
Let's analyze the options:
In option F we have:
[tex]2x+24\text{ and }2(x+4)[/tex]We need to use distributive property on the second expression and check if we get the same as in the first of the expressions.
[tex]2(x+4)[/tex]Distributive property tells us to multiply the outside number by both of the terms inside the parenthesis:
[tex]2\cdot x+2\cdot4[/tex]Solving the multiplications:
[tex]2x+8[/tex]This is different from 2x+24, so the expressions are not equivalent.
In Option G we have:
[tex]9+3x\text{ and }3(3+x)[/tex]Using distributive property on the second expression:
[tex]3(3+x)=3\cdot3+3\cdot x=9+3x[/tex]As we can see, the second expression is 9+3x, which is also the first expression, this means that the expressions are EQUIVALENT.
Answer: G
[tex]9+3x\text{ and }3(3+x)[/tex]
