How so I solve for "n" in the equation. I keep getting different answers and when I check the answer inserted in the equation it doesn't match up

## -37/24= 1/2n+1/3

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# 2 Answers

Hi Ellie;

-37/24= (1/2)n+1/3

Fractions are so annoying and confusing. Let's get rid of these...

The denominators are 24, 2 and 3.

Let's multiply both sides by 24...

(24)(-37/24)=(24)[(1/2)n+1/3]

-37=12n+8

Let's subtract 8 from both sides...

-8-37=12n+8-8

-45=12n

Let's divide both sides by 12...

-45/12=(12n)/12

-45/12=n

**-15/4=n**

Let's check our results...

-37/24= (1/2)n+1/3

-37/24= [(1/2)(-15/4)]+1/3

-37/24=(-15/8)+1/3

Let's note the fact that (1/3)(8/8)=8/24.

Let's note the fact that (-15/8)(3/3)=-45/24

-37/24=(-45/24)+(8/24)

The denominators are identical. These cancel...

-37=-45+8

-37=-37

I'm assuming you mean -37/24=(1/2)n+(1/3)

subtract 1/3 from both sides

(-37/24)-(1/3)=(1/2)n+(1/3)-(1/3)

(-37/24)-(8/24)=(1/2)n

(-45/24)=(1/2)n

multiply both sides by 2

(2)(-45/24)=(2)(1/2)n

-90/24=n

simplify

-45/12=n, or

-3 9/12=n

-3 3/4=n