Question

2/9z - 5/3 = 3/4 solve for z

Answer 1

`z = (87)/(8) = 10.875`

Explanation:

Assuming we have
`(2)/(9) z - (5)/(3) = (3)/(4)`,

You must first add 5/3 on both sides to cancel the 5/3 side.

`(2)/(9) z - (5)/(3) + ((5)/(3) )= (3)/(4) + ((5)/(3) )`

`(2)/(9) z = (3)/(4) + (5)/(3)`

This isolates the variable z on the other side.

You them must simplify the expression by finding the least common denominator. In this case, you can multiply 3/4 by 3/3 and 5/3 by 4/4 so that the denominator will be left as 12.

`(2)/(9) z = (3)/(4) ((3)/(3))+ (5)/(3)((4)/(4))`

`(2)/(9) z = (9)/(12) + (20)/(12)`

Then, add the numerators on the right side.

`(2)/(9) z = (29)/(12)`

Now, you can multiply each side by 9/2 to cancel the 2/9 on the left side to isolate z. This method is commonly referred to as "keep change flip" when you divide with a fraction. When multiplying fraction, you can multiply straight across the numerator and denominator.

`(2)/(9) ((9)/(2)) z = (29)/(12) ((9)/(2) )`

`(1)z = (261)/(24)`

Simplified,
`z = (87)/(8) = 10.875`