Question

For what values of a is the sum of the fractions 2a−1 / 4 and a−1 /3 positive?

Answer 1

`a>(7)/(10)`

Explanation:

We are given fractions as

`(2a-1)/(4)`

`(a-1)/(3)`

now, we can add both fractions

`(2a-1)/(4)+(a-1)/(3)`

we can see that both denominators are different

so, we can find common denominator

`(3* (2a-1))/(3* 4)+(4*(a-1))/(4* 3)`

`(3* (2a-1)+4*(a-1))/(3* 4)`

now, we can combine them

`(6a-3+4a-4)/(3* 4)`

`(10a-7)/(12)`

To make it positive, both numerator and denominator must be positive

Since, bottom is 12 ...which is positive

so, numerator should also be positive

so, we get

`10a-7>0`

now, we can solve for a

we get

`a>(7)/(10)`