math simplification problem ALGEBRA?

(5/6)z+(4/3)=-(5/3)z-(1/8)

Combine like terms:

(5/6)z+(5/3)z= -1/8 - 4/3

5z/6 + 5z/3 = -1/8 - 4/3

5z/6 + (5z*2 / 3*2) = -1/8 - 4/3

5z/6 + 10z/6 = (-3-32)/24

(5z+10z)/6 = -35/24

15z/6 = -35/24

15z * 24 = 6 * -35

360z = -210

z=-210/360

z=-7/12

.....

Either multiply the whole thing by 24 to eliminate the fractions, or rewrite the fractions so that they have the same denominator of 24.

Either way, you get, either for the whole thing or for the numerators:

(5*4)z + (4*8) = (-5*8)z - 3

20z + 32 = -40z - 3

20z + 40z = -3 - 32

60z = -35

z = -35/60 = -7/12

5/6z +4/3 = - 5/3z - 1/8

MULTIPLY BOTH SIDES BY 24

20z + 32 = -40z - 3

60z = -35

z = -35/60 = - 7/12 ANSWER

(5/6)z+(4/3)=-(5/3)z-(1/8) or

5/6z+5/3z = -1/8 - 4/3 = -35/24 or

15/6z = -35/24 or

z = -(35/24) * (6/15) = -7/12 <= ANS