## RealityWillSlapYou Group Title Is this correct? 12 + 4x ≤ 5x -2 12 -x ≤ -2 -x ≤ -14 one year ago one year ago

1. JamesJ Group Title

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

2. RealityWillSlapYou Group Title

Oh, okay so it's x ≤ -14?

3. JamesJ Group Title

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

4. RealityWillSlapYou Group Title

?

5. JamesJ Group Title

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.

6. RealityWillSlapYou Group Title

Okay, so is all of it wrong?

7. JamesJ Group Title

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 $x \geq 14$

8. RealityWillSlapYou Group Title

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

9. JamesJ Group Title

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.

10. RealityWillSlapYou Group Title

Closed circle shade to the right?

11. JamesJ Group Title

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

12. JamesJ Group Title

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.

13. RealityWillSlapYou Group Title

Okay, thank you so much! ｏ(￣∇￣ｏ)