Answer:
[tex]a>\frac{7}{10}[/tex]
Step-by-step explanation:
We are given fractions as
[tex]\frac{2a-1}{4}[/tex]
[tex]\frac{a-1}{3}[/tex]
now, we can add both fractions
[tex]\frac{2a-1}{4}+\frac{a-1}{3}[/tex]
we can see that both denominators are different
so, we can find common denominator
[tex]\frac{3\times (2a-1)}{3\times 4}+\frac{4\times(a-1)}{4\times 3}[/tex]
[tex]\frac{3\times (2a-1)+4\times(a-1)}{3\times 4}[/tex]
now, we can combine them
[tex]\frac{6a-3+4a-4}{3\times 4}[/tex]
[tex]\frac{10a-7}{12}[/tex]
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
[tex]10a-7>0[/tex]
now, we can solve for a
we get
[tex]a>\frac{7}{10}[/tex]
