Inequality with Fractions

[sammymt53]

I have a question on a problem, I am having troubles with. 7x> 1/15. I am lost with this one. I know the > stays, but the rest I cannot figure if the answer is 7/15 or 15/7. I missed something along the way.

 

[Mrspi]

I have a question on a problem, I am having troubles with. 7x> 1/15. I am lost with this one. I know the > stays, but the rest I cannot figure if the answer is 7/15 or 15/7. I missed something along the way.

You have 7x on the left side. You would like to have 1x, or just x. If we multiply (1/7)*7, we get 1, right? So, let's multiply both sides of the inequality by (1/7). Multiplying both sides of an inequality by a POSITIVE number does not affect the direction of the inequality symbol, so you're correct in saying "the > stays":

7x > (1/15)

(1/7)*(7x) > (1/7)*(1/15)

1x > (1/7)*(1/15)

x > (1/7)*(1/15)

Now, all you need to do is multiply those two fractions together. You may need to review some basic arithmetic...to multiply fractions together, you multiply the numerators, and you multiply the denominators.

A Google search for "lessons on multiplying fractions" should provide you with lots of opportunities to review!

 

[HallsofIvy]

The point is that you don't just do things at random or just memorize formulas without understanding. To "solve" an inequality or equation for x you need to get "x" by itself. In the given inequality, x is not by itself because it is multiplied by 7. To get x by itself, divide both sides of the inequality by 7 or,equivalently, multiply by 1/7. As Mrspi said, because you are multiplying (or dividing) both sides by a positive number, you do not change the direction of the inequality.

The correct answer is neither 15/7 or 7/15.

 

[Deleted member 4993]

AHEM...hope Subhotosh doesn't send me to the corner...:???:

Only if you come to play cricket with me.....

Anyway, I personally agree with your process - may be some true-blue mathematician will violently object - but not me......