-6<9+3y<6
9+3y>-6
y>-5
9+3y<6
y<-1
On a number line, dot -1 and -5. Is this right?
3f>15 or 2f<-4
15>3f
f>5
2f<-4
F<-2
Is this right?
Yes, both are correct. In the second question, you have an either/or answer. Both inequalities cannot simultaneously be true.
is the second question right?
Yes, but only because of the "or" in the second question.
Yes, you have correctly solved the inequalities in both cases.
For the first set of inequalities, -6 < 9 + 3y < 6, you correctly performed the operations to isolate 'y' in each inequality. This resulted in y > -5 for 9 + 3y > -6, and y < -1 for 9 + 3y < 6.
To represent these solutions on a number line, you would mark a dot at -1 to represent y < -1, and another dot at -5 for y > -5. Since these are strict inequalities (< and >), you would use open circles at -1 and -5 to denote that those specific values are not included in the solution set.
For the second set of inequalities, 3f > 15 or 2f < -4, you applied the same technique by isolating 'f' in each inequality. This led to f > 5 for 15 > 3f, and f < -2 for 2f < -4.
Representing these solutions on a number line would involve placing a dot at 5 to represent f > 5, and another dot at -2 for f < -2. Again, since these are strict inequalities, you would use open circles at 5 and -2 to indicate that those values are not part of the solution set.