Question

What are the solution intervals for |2x – 1| + 6 > 9?

Answer 1

\[|2x-1|+6>9\iff |2x-1|>9-6
\\\iff |2x-1|>3
\\\iff 2x-1>3\quad\text{or}\quad 2x-1<-3
\\\iff 2x>3+1\quad\text{or}\quad 2x<-3+1
\\\iff 2x>4\quad\text{or}\quad 2x<-2\\
\iff x>2\quad\text{or} \quad x<-1

\]
So :
\[S=]-\infty,-1[\cup]2,+\infty[.\]