How many solutions does the following equation have?

|3x + 12| = 18

No solution
One solution
Two solutions
Infinitely many solutions

Question

How many solutions does the following equation have?

|3x + 12| = 18

 No solution
 One solution
 Two solutions
 Infinitely many solutions

nuccioreggie · Answer

@Michele_Laino

michele_laino · Answer

we have to distinguish two cases, namely such equation is equivalent to these systems:

$$\Large  \left\{ \begin{gathered}
  3x + 12 = 18 \hfill \
   \hfill \
  3x + 12 \geqslant 0 \hfill \ 
\end{gathered}  \right. \cup \left\{ \begin{gathered}
   - \left( {3x + 12} \right) = 18 \hfill \
   \hfill \
  3x + 12 < 0 \hfill \ 
\end{gathered}  \right.$$

nuccioreggie · Answer

So its B

michele_laino · Answer

please wait, I'm doing some computation

michele_laino · Answer

no, I'm sorry, it is not option B

nuccioreggie · Answer

Oh wait i ment C

michele_laino · Answer

that's right!

michele_laino · Answer

from my computation, I got two distinct solutions