Is this correct?

12 + 4x ≤ 5x -2
12 -x ≤ -2
-x ≤ -14

Question

Is this correct?

12 + 4x ≤ 5x -2
12 -x ≤ -2
-x ≤ -14

jamesj · Answer

Yes, but we would never express the answer that way. You want an inequality involving only x, not -x, hence ....

x ....

realitywillslapyou · Answer

Oh, okay so it's x ≤ -14?

jamesj · Answer

No. Careful. a < b <=> -a > -b

realitywillslapyou · Answer

?

jamesj · Answer

if 
$$ -x \leq -14 $$
that can NOT mean that $ x \leq -14 $. 

For example, when x = 15, $ -x = 15 \leq -14 $ is true, but $ x =15 \leq -14 $ is definitely false.

realitywillslapyou · Answer

Okay, so is all of it wrong?

jamesj · Answer

No. What I am saying is you want to have an inequality involving only x, not -x.

The inequality 
$$ -x \leq -14 $$
is equivalent to
$$ x \geq 14 $$

realitywillslapyou · Answer

Oh, okay I get it now. So I should shade it to the left, correct?

jamesj · Answer

No. x is greater or equal to 14, so it is that part of the number line to the right of 14, including 14 itself.

realitywillslapyou · Answer

Closed circle shade to the right?

jamesj · Answer

Yes, as the shaded circle indicates you include that value, in this case 14.

jamesj · Answer

btw, whenever you do these things you should double check with the original expression.  Put in x = 14 and x = 15 and make sure you get the results you expect.

realitywillslapyou · Answer

Okay, thank you so much! ｏ(￣∇￣ｏ)