Solve for n. `12(1/4-n/3)lt=-6n`

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justaguide eNotes educator| Certified Educator

The inequality `12(1/4 - n/3) <= -6*n` has to be solved for n. To solve remember that any operation performed for both the sides with a positive number does not change the sign between the sides of the inequality.

`12(1/4 - n/3) <= -6*n`

=> `(12/4 - (12*n)/3) <= -6*n`

=> `3 - 4*n <= -6*n`

=> `3 <= -2*n`

Multiplying the sides with a negative number or dividing them by a negative number changes the sign between the sides.

=> `-3/2 >= n`

The solution of the inequality is `n <= -3/2`

plymouth50 | Student

thank you so much...I thought that was it...just seemed too easy...the teacher said something about switching the inequality sign..but I can't remember why?  Now I'm afraid I have to go back and change them in all the other problems.

Thanks again for taking the time to answer my question!  I get it now!  Great explaining!

abalony | Student

Problem: 12(1/4-n/3) >= -6n

Step 1, distribute the 12: 3- 4n >= -6n

Step 2, add 4n to both side: 3 >= -2n

Step 3, divide by -2 (notice the change of direction of the inequality):

-3/2 <= n


And that's the answer.

 

plymouth50 | Student

thank you so much...I thought that was it...just seemed too easy...the teacher said something about switching the inequality sign..but I can't remember why?  Now I'm afraid I have to go back and change them in all the other problems.

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