QUICKKKKKKKKFor what values of a is the sum of the fractions (2a−1)/4 and (a−1)/3 positive?
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Whatever% of anything is just (whatever/100) * anything.
let's say we'll add "x" cups of pure vinegar, pure vinegar meaning is 100% vinegar.
how much vinegar is there in "x" cups of 100% vinegar? well (100/100) * x, or just "x".
how much vinegar is there in 10 cups of 10% vinegar? well, (10/100) * 10, or just 1.
say after adding the "x" cups to the 10 cups, we end up with "y" cups, of 50% of vinegar.
how much is 50% of y? well, (50/100) * y or 0.5y.
bearing in mind that x+10 = y, both cups amounts added up, and that x+1=0.5y, both vinegar amounts added up, thus
let's say we'll add "x" cups of pure vinegar, pure vinegar meaning is 100% vinegar.
how much vinegar is there in "x" cups of 100% vinegar? well (100/100) * x, or just "x".
how much vinegar is there in 10 cups of 10% vinegar? well, (10/100) * 10, or just 1.
say after adding the "x" cups to the 10 cups, we end up with "y" cups, of 50% of vinegar.
how much is 50% of y? well, (50/100) * y or 0.5y.
bearing in mind that x+10 = y, both cups amounts added up, and that x+1=0.5y, both vinegar amounts added up, thus
We know that .
And .
Hope this helps.