Question

which two expressions are equivalent F. 2× +24 and 2(×+4 G. 9+3× and 3(3+× H. 4(×-1) and 4×-14 J 5(2x-1) and 5x-5

Answer 1

The expressions we have are:

`\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}`

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:

`2x+24\text{ and }2(x+4)`

We need to use distributive property on the second expression and check if we get the same as in the first of the expressions.

`2(x+4)`

Distributive property tells us to multiply the outside number by both of the terms inside the parenthesis:

`2\cdot x+2\cdot4`

Solving the multiplications:

`2x+8`

This is different from 2x+24, so the expressions are not equivalent.

In Option G we have:

`9+3x\text{ and }3(3+x)`

Using distributive property on the second expression:

`3(3+x)=3\cdot3+3\cdot x=9+3x`

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

`9+3x\text{ and }3(3+x)`