Question

If $\frac{9u-11}{2} = \frac{19u+11}{3}$, what is the value of $u$?

Answer 1

Key Ideas

• Solving algebraic equations involving fractions
• Cross multiplication

Solving the Question

We're given:

`$(9u-11)/(2) = (19u+11)/(3)`

⇒ First, let's get rid of the fractions by multiplying both sides by 2 and 3:

`(9u-11)/(2)*2 = (19u+11)/(3)*2\\\\9u-11= (2(19u+11))/(3)\\\\3(9u-11)= (2(19u+11))/(3)*3\\\\3(9u-11)= 2(19u+11)`

⇒ Expand the parentheses:

`27u-33= 38u+22`

⇒ Isolate u:

`27u-38u= 22+33\\-11u= 55\\u=-5`

Answer

u = -5