# Solve for z z/3+5=z/7+1 z3+5=z7+1
Move all terms containing z to the left side of the equation.
Subtract z7 from both sides of the equation.
z3+5-z7=1
To write z3 as a fraction with a common denominator, multiply by 77.
z3⋅77-z7+5=1
To write -z7 as a fraction with a common denominator, multiply by 33.
z3⋅77-z7⋅33+5=1
Write each expression with a common denominator of 21, by multiplying each by an appropriate factor of 1.
Multiply z3 and 77.
z⋅73⋅7-z7⋅33+5=1
Multiply 3 by 7.
z⋅721-z7⋅33+5=1
Multiply z7 and 33.
z⋅721-z⋅37⋅3+5=1
Multiply 7 by 3.
z⋅721-z⋅321+5=1
z⋅721-z⋅321+5=1
Combine the numerators over the common denominator.
z⋅7-z⋅321+5=1
Simplify each term.
Simplify the numerator.
Factor z out of z⋅7-z⋅3.
Factor z out of z⋅7.
z(7)-z⋅321+5=1
Factor z out of -z⋅3.
z(7)+z(-1⋅3)21+5=1
Factor z out of z(7)+z(-1⋅3).
z(7-1⋅3)21+5=1
z(7-1⋅3)21+5=1
Multiply -1 by 3.
z(7-3)21+5=1
Subtract 3 from 7.
z⋅421+5=1
z⋅421+5=1
Move 4 to the left of z.
4z21+5=1
4z21+5=1
4z21+5=1
Move all terms not containing z to the right side of the equation.
Subtract 5 from both sides of the equation.
4z21=1-5
Subtract 5 from 1.
4z21=-4
4z21=-4
Multiply both sides of the equation by 214.
214⋅4z21=214⋅-4
Simplify both sides of the equation.
Simplify 214⋅4z21.
Cancel the common factor of 21.
Cancel the common factor.
214⋅4z21=214⋅-4
Rewrite the expression.
14⋅(4z)=214⋅-4
14⋅(4z)=214⋅-4
Cancel the common factor of 4.
Factor 4 out of 4z.
14⋅(4(z))=214⋅-4
Cancel the common factor.
14⋅(4z)=214⋅-4
Rewrite the expression.
z=214⋅-4
z=214⋅-4
z=214⋅-4
Simplify 214⋅-4.
Cancel the common factor of 4.
Factor 4 out of -4.
z=214⋅(4(-1))
Cancel the common factor.
z=214⋅(4⋅-1)
Rewrite the expression.
z=21⋅-1
z=21⋅-1
Multiply 21 by -1.
z=-21
z=-21
z=-21
Solve for z z/3+5=z/7+1

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