## RealityWillSlapYou 2 years ago Is this correct? 12 + 4x ≤ 5x -2 12 -x ≤ -2 -x ≤ -14

1. JamesJ

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

2. RealityWillSlapYou

Oh, okay so it's x ≤ -14?

3. JamesJ

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

4. RealityWillSlapYou

?

5. JamesJ

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

Okay, so is all of it wrong?

7. JamesJ

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

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

9. JamesJ

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

Closed circle shade to the right?

11. JamesJ

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

12. JamesJ

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

Okay, thank you so much! ｏ(￣∇￣ｏ)