Here's the question you clicked on:
RealityWillSlapYou
Is this correct? 12 + 4x ≤ 5x -2 12 -x ≤ -2 -x ≤ -14
Yes, but we would never express the answer that way. You want an inequality involving only x, not -x, hence .... x ....
Oh, okay so it's x ≤ -14?
No. Careful. a < b <=> -a > -b
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.
Okay, so is all of it wrong?
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 \[ x \geq 14 \]
Oh, okay I get it now. So I should shade it to the left, correct?
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.
Closed circle shade to the right?
Yes, as the shaded circle indicates you include that value, in this case 14.
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.
Okay, thank you so much! ｏ(￣∇￣ｏ)