# SAT Math : How to solve for a variable as part of a fraction

## Example Questions

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### Example Question #1155 : Algebra

Solve:

Explanation:

We want to isolate the x. First, we take away 3 from both sides. Then we have:

To get x by itself, we multiply by the reciprocal on both sides.

Then, we have:

### Example Question #7 : How To Solve For A Variable As Part Of A Fraction

If  , then what is the value of ?

9/114

7/12

38/3

none of these

3/38

38/3

Explanation:

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

Find x.

None

Explanation:

Cross multiply:

### Example Question #1 : How To Solve For A Variable As Part Of A Fraction

The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.

Explanation:

Let numerator = N and denominator = D.

According to the first statement,

N = (D x 5) + 4.

According to the second statement, N / 2 = 3 * D.

Let's multiply the second equation by –2 and add itthe first equation:

–N = –6D

+[N = (D x 5) + 4]

=

–6D + (D x 5) + 4 = 0

–1D + 4 = 0

D = 4

Thus, N = 24.

Therefore, N/D = 24/4 = 6.

Solve for x: