Solve the equation and explain

Start by simplifying the equation by cross multiplying

9(z+1) = 3z

then distribute 9 into the brackets

9z + 9= 3z

then move the constant to the right hand side and change its sign

9z = 3z -9

then move the variable to the left hand side and change its sign

9z - 3z = -9

collect like terms

6z = - 9

then divide both equations by 6 to get z by itself

z = -9/6

simplify the fraction

z = -3/2