Question

Easy variable question pls help

Answer 1

z = -4 1/2

Explanation:

1. First change the mixed fractions to improper fractions so it's easier

`(16)/(5\\)/(z-(1)/(2)) = (8)/(3)/(z+(1)/(3))`

2. Simplify

`(32)/(5(2z-1)) = (8)/(3z+1)`

3. Cross multiply

`32(3z+1) = 5(2z-1) * 8`

4. Simplify again (distributive property)

`32(3z+1) = 40(2z-1)`

5. Distributive property

`32(3z+1) -> 96z+32`

`40(2z-1) -> 80z-40`

`96z+32=80z-40`

6. Subtract 32 from both sides

`96z+32-32 = 80z-40-32`

7. Simplify

`96z = 80z-72`

8. Subtract 80 from both sides

`96z-80z=80z-72-80z`

9. Simplify

`16z=-72`

10. Divide both sides by 16

`(16z)/(16)=(-72)/(16)`

11. Simplify

`z=-(9)/(2) -> also = -4(1)/(2)`

Sorry if it was too long but hope this helps! :)

And also try using symbolab cuz it gives step by step explanations it's really good!