I thought of a number, multiplied it by 2 1/2, divided the result by 1 1 / 5, subtracted 7/18 from it, and got 1 5/6. What was my number?

X=88/45

(2.5x / (11/5)) - (7/18) = (11/6) - Equation

(12.5x/11) - (7/18) = (11/6) - Multiply 2.5*5 = 12.5

(125x/11) - (35/9) = (55/3) - Multiply both sides by 10

(125x/11) = (200/9) - Add (35/9) to both sides

125x = (2200/9) - Multiply both sides by 11

x = (88/45) - Divide both sides by 125