Question

)lf V2x - 4 - V3x – 8, what is the value of x?A) 1B) 2.C) 4D) 8

Answer 1

`C)4`

1) Since we have a radical equation, we'll need probably to verify if the solution is valid. In Radical equations, extraneous solutions happen a lot. So let's solve this:

`\begin{gathered} √(2x-4)=√(3x-8) \\ (√(2x-4))^2=(√(3x-8))^2 \\ 2x-4=3x-8 \\ 2x-4+4=3x-8+4 \\ 2x=3x-4 \\ 2x-3x=3x-4-3x \\ -x=-4 \\ x=4 \end{gathered}`

2) Let's now verify if this solution is correct since we need to avoid extraneous solutions:

`\begin{gathered} √(2x-4)=√(3x-8) \\ √(2(4)-4)=√(3(4)-8) \\ √(4)=√(4) \\ 2=2\:True! \end{gathered}`