Help with linear inequalities...?

Question

Need help solving:
1/2 - m/12 is less than or equal to 7/12

If I didn't have a variable in a fraction, I would multiply each side by 24, so get rid of the fractions. When the variable is thrown in, I'm totally lost. Can someone explain to me how to get rid of the fractions. I would think it's this:

12 - m/24 is less than or equal to 14

Answer 1

1/2 - m/12 <= 7/12

To solve this, all you have to do is treat it like an equation and isolate m. In this case, we multiply both sides by 12.

12(1/2 - m/12) <= 12(7/12)

And note how this gets rid of all fractions, leaving behind:

6 - m <= 7

Now, bring the 6 over to the right hand side.

-m <= 1

And now, multiply both sides by (-1). This is the *only* difference when solving inequalities and equalities; multiplying or dividing by a negative number flips the inequality sign.

m >= 1

And that's your answer.

Answer 2

1/2 - m/12 is less than or equal to 7/12

bring m to one side of the inequi. and the numbers to other side

1/2 - m/12 <= 7/12

1/2 <= 7/12 + m/12

1/2 - 7/12 <= m/12

- 6 / 12 <= m/12

-6 <= m