Question

Choose all equivalent equations to the following:X +5=20 + 2x1. X+20=5 2. X= -15 3. 5+3x=20 4. x-15=2x 5. 3x=25 6. 3x=-15

Answer 1

You have the following equation:

`x+5=20+2x\text{ (1)}`

In order to know which of the given eqaution are equivalent to the previous one, you proceed as follow:

1. In the first case, x + 20 = 5, this equation is not equivalent because it is not possible to get the equation from the equation (1).

2. To know if it is equivalent you solve the equation (1) for x:

`\begin{gathered} x+5=20+2x \\ x-2x=20-5 \\ -x=15 \\ x=-15 \end{gathered}`

Then, the equation x=-15 is equivalent.

3. For the equation 5x + 3x = 20, you solve for x:

`\begin{gathered} 5x+3x=20 \\ 8x=20 \\ x=(20)/(8)=(5)/(2) \end{gathered}`

Then, it is not equivalent

4.

`\begin{gathered} x-15=2x \\ x-2x=15 \\ -x=15 \\ x=-15 \end{gathered}`

Then, x-15=2x is equivalent

5.

`\begin{gathered} 3x=25 \\ x=(25)/(3) \end{gathered}`

Then, it not equivalent.

`\begin{gathered} 3x=-15 \\ x=(-15)/(3)=-5 \end{gathered}`

Then, it is not equivalent