Question

3. Select ALL the equations that have the same solution as 2x - 5 = 15:2x = 102x = 202(x - 5) = 152x - 20 = 04x - 10 = 3015 = 5 - 2x

Answer 1

Starting from:

`2x-5=15`

Let's check the first two equations. For this, we want to put "2x" alone in the left side. So let's move "-5" to the other side by adding 5 in both sides:

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

So,

2x = 10 -> incorrect.

2x = 20 -> correct.

To check the thirs one, let's rewrite it and apply the distributive property on the parenthesis:

`\begin{gathered} 2(x-5)=15 \\ 2x-10=15 \end{gathered}`

We can see that the right side is the same, but the left side is not, so this is not the same and won't have the same solution.

So,

2(x-5) = 15 -> incorrect.

To check the fourth , we start, again from our equation, we can pass the "1% to the right side:

`\begin{gathered} 2x-5=15 \\ 2x-5-15=15-15 \\ 2x-20=0 \end{gathered}`

We can see that it is equivalent to the fourth equation, so it will give the same solution.

So,

2x - 20 = 0 -> correct.

For the fifth, we can see that each term is double the term of the 2x - 5 = 15, so if we divide both sides by 2, we will get the same equation:

`\begin{gathered} 4x-10=30 \\ (4x-10)/(2)=(30)/(2) \\ (4x)/(2)-(10)/(2)=15 \\ 2x-5=15 \end{gathered}`

Since the equations are equivalent, they have the same solution.

So,

4x - 10 = 30 -> correct.

The last one has the sides switched, so let's start by switching sides:

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

Right side is the same, but the left side is not, because it has inverted sign:

`\begin{gathered} 5-2x=15 \\ -(2x-5)=15 \end{gathered}`

So, this is not equivalent.

So,

15 = 5 - 2x -> incorrect.

So, from the presented equations, the only that have the same solution as 2x - 5 = 15 are:

2x = 20

2x - 20 = 0

4x - 10 = 30