Question

Choose all of the equations that have only 1 solution.

Answer 1

1)

`\begin{gathered} 2(2+5x)=3x+14 \\ \Rightarrow4+10x=3x+14 \\ \Rightarrow7x=10 \end{gathered}`

Option 1 has only one solution,

2)

`\begin{gathered} 3x+5=2x-4 \\ \Rightarrow x=-9 \end{gathered}`

Option 2 has only one solution

3)

`\begin{gathered} 6x-4=3(2x-5) \\ \Rightarrow6x-4=6x-15 \\ \Rightarrow-4=-15!!! \end{gathered}`

Option 3 does not have any valid solutions.

4)

`\begin{gathered} -5+7x=7x-5 \\ \Rightarrow-5=-5 \end{gathered}`

Option 4 has an infinite number of solutions, not only one.

5)

`\begin{gathered} 5x+4+2x=4x-5+7x \\ \Rightarrow7x+4=11x-5 \\ \Rightarrow4x=9 \end{gathered}`

Therefore, option 5 has only one solution.

The equations that have only one solution are options 1, 2, and 5 (top to bottom).