When do you change the equality sign when solving a inequality??

Question

The question is 1-2X>1/3 is it x > 1/3 or x<1/3. Provided I solved it correctly.lol.

Answer 1

Ya, like above plus:

I was taught math by moving terms and changing their sign. Hence, why must you do the sign switch when mult or div?

Here's an example:

5 - 5x < 10


The way you'd normally do it is:

- 5x < 5
x > -1

I do it:
5 - 5x <10
5 - 10 < 5x
-5 < 5x
-1 < x

Same answer, but you don't have to divide by negatives, hence don't need to change the sign. However, with refrence to 'x', the sign did change ;).

Answer 2

you change the "direction" of an inequality sign when multiplying or dividing by a negative value...
1- 2x > 1/3
-2x > -2/3
x < 1/3

check your answer...pick a value less than 1/3

1 - 2*(1/4) >? 1/3
1 - 2/4 >? 1/3
1/2 > 1/3

so it seems

Answer 3

x < 1/3

because

1 - 2x > 1/3
3 - 6x > 1 <---multiply by 3
- 6x > - 2 <---subtract 3
x < 1/3 <--- divide by -6, and reverse sign

The sign gets reversed when you multiply or divide by a negative numer. Since the final step is dividing by -6, it is necessary to change the sign.