Question

Solve the inequality and specify the answer using interval notation.

6 − 3x ≤ 24


[−6, 6]

(−6, )

(−, −6)

[−6, )

(−, −6]

Answer 1

I assume those blank spots are infinity since I would dream that the symbol for infinity wouldn't copy well.

So your job is to isolate x!
To do that first you need to undo the addition by 6, by subtracting 6 on both sides of the inequality.

\[6-3x \le 24 \]
-6 -6
So we have
\[-3x \le 18 \]
Now remember we are still trying to get x by itself. The last undo we need to do is the multiplication by -3. To undo multiplication by -3 we need to do division by -3 on both sides of the inequality.
When we do this, don't forget to flip the inequality.
Remember when you multiply or divide both sides of inequality by a negative number you will have to flip the inequality sign (ex. -3<-2 by multiply both sides by -1
we have 3>2 <-----see how the inequality sign needed flipping)
\[x \ge \frac{18}{-3}\]

Answer 2

Thanks so much for helping! n Yes, they are infinity signs.
So I would be left with x\[\ge -6 \] right? I'm still not sure but I think the answer would be [- (infinity) 6) I'm not sure

Answer 3

so we have x greater than or equal to -6
thats means it can be -6 or bigger
so [-6,inf)

Answer 4

Oh, okay I see.. thank you:D