Respuesta :
[tex]\lvert6x-9\rvert+6<3[/tex]
When you have a absolute value in a inequality, to solve:
1. Leave the absolute value in one side of the inequality sing and the other terms in the other side:
-Substract 6 in both sides of the inequatily:
[tex]\begin{gathered} \lvert6x-9\rvert+6-6<3-6 \\ \lvert6x-9\rvert<-3 \end{gathered}[/tex]2. As the abosule value is less than a negative number you have no solution for the system, you can see it by following the next steps:
-Write the inequality as two inequalities, one with the sing < and the other with the sing >:
[tex]\begin{gathered} 6x-9<-3 \\ \\ 6x-9>-3 \end{gathered}[/tex]Solve the first inequality:
[tex]\begin{gathered} 6x-9<-3 \\ 6x-9+9<-3+9 \\ 6x<6 \\ \frac{6}{6}x<\frac{6}{6} \\ \\ x<1 \end{gathered}[/tex]Solve the secodn inequality:
[tex]\begin{gathered} 6x-9>-3 \\ 6x-9+9>-3+9 \\ 6x>6 \\ \frac{6}{6}x>\frac{6}{6} \\ \\ x>1 \end{gathered}[/tex]If you combine those solutions you get:
[tex]1As you can see the system has no solution as x cannot be less than 1 and greather than 1 at the same time.Then, the inequality doesn't have solution