So you think that x = -5 is the solution for the inequality? Let's check it out.
(Check)
- Substitute x = -5 in the inequality
[tex]-6<3(-5)+9<21\\-6<-15+9<21\\-6<-6<21[/tex]
If it was the symbol ≤ you'd be correct, but it's < so It's a bit wrong.
Now let's solve the inequality. Separate the inequality by parts.
[tex]\left \{ {{-6<3x+9} \atop {3x+9<21}} \right. \\\left \{ {{-6-9<3x} \atop {3x<21-9}} \right. \\\left \{ {{-15<3x} \atop {3x<12}} \right. \\\left \{ {{x>-5} \atop {x<4}} \right.[/tex]
Therefore, the inequality is true only when x > -5 or x < 4.
(Check)
- Substitute x = -4 in the inequality.
[tex]-6<3(-4)+9<21\\-6<-12+9<21\\-6<-3<21[/tex]
The inequality is true for first case.
- Substitute x = 3 in the inequality
[tex]-6<3(3)+9<21\\-6<9+9<21\\-6<18<21[/tex]
The inequality is true for second case.
So the answer for inequality is -5 < x < 4
That means only {-4, -3, -2, ..., 3} can make the inequality true.
