blank/5 - 1/2 = 3/blank
To find the value of blank, let's solve the equation step by step:
blank/5 - 1/2 = 3/blank
To get rid of denominators, let's multiply through by the LCD (Least Common Denominator) which is 10:
10 * (blank/5) - 10 * (1/2) = 10 * (3/blank)
2(blank) - 5 = 30/blank
Multiplying both sides by blank to eliminate the fraction:
2(blank) * blank - 5 * blank = 30
2(blank^2) - 5(blank) = 30
2blank^2 - 5blank - 30 = 0
Now, we have a quadratic equation. Let's solve it by factoring:
(2blank + 3)(blank - 10) = 0
Setting each factor equal to zero:
2blank + 3 = 0 or blank - 10 = 0
For 2blank + 3 = 0:
2blank = -3
blank = -3/2
For blank - 10 = 0:
blank = 10
So, the possible solutions for blank are -3/2 or 10.