# Solve for z 4/z=18/(5z)+2 4z=185z+2
Find the LCD of the terms in the equation.
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
z,5z,1
Since z,5z,1 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,5,1 then find LCM for the variable part z1,z1.
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number 1 is not a prime number because it only has one positive factor, which is itself.
Not prime
Since 5 has no factors besides 1 and 5.
5 is a prime number
The number 1 is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of 1,5,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.
5
The factor for z1 is z itself.
z1=z
z occurs 1 time.
The LCM of z1,z1 is the result of multiplying all prime factors the greatest number of times they occur in either term.
z
The LCM for z,5z,1 is the numeric part 5 multiplied by the variable part.
5z
5z
Multiply each term by 5z and simplify.
Multiply each term in 4z=185z+2 by 5z in order to remove all the denominators from the equation.
4z⋅(5z)=185z⋅(5z)+2⋅(5z)
Simplify 4z⋅(5z).
Rewrite using the commutative property of multiplication.
54zz=185z⋅(5z)+2⋅(5z)
Multiply 54z.
Combine 5 and 4z.
5⋅4zz=185z⋅(5z)+2⋅(5z)
Multiply 5 by 4.
20zz=185z⋅(5z)+2⋅(5z)
20zz=185z⋅(5z)+2⋅(5z)
Cancel the common factor of z.
Cancel the common factor.
20zz=185z⋅(5z)+2⋅(5z)
Rewrite the expression.
20=185z⋅(5z)+2⋅(5z)
20=185z⋅(5z)+2⋅(5z)
20=185z⋅(5z)+2⋅(5z)
Simplify each term.
Rewrite using the commutative property of multiplication.
20=5185zz+2⋅(5z)
Cancel the common factor of 5.
Factor 5 out of 5z.
20=5185(z)z+2⋅(5z)
Cancel the common factor.
20=5185zz+2⋅(5z)
Rewrite the expression.
20=18zz+2⋅(5z)
20=18zz+2⋅(5z)
Cancel the common factor of z.
Cancel the common factor.
20=18zz+2⋅(5z)
Rewrite the expression.
20=18+2⋅(5z)
20=18+2⋅(5z)
Multiply 5 by 2.
20=18+10z
20=18+10z
20=18+10z
Solve the equation.
Rewrite the equation as 18+10z=20.
18+10z=20
Move all terms not containing z to the right side of the equation.
Subtract 18 from both sides of the equation.
10z=20-18
Subtract 18 from 20.
10z=2
10z=2
Divide each term by 10 and simplify.
Divide each term in 10z=2 by 10.
10z10=210
Cancel the common factor of 10.
Cancel the common factor.
10z10=210
Divide z by 1.
z=210
z=210
Cancel the common factor of 2 and 10.
Factor 2 out of 2.
z=2(1)10
Cancel the common factors.
Factor 2 out of 10.
z=2⋅12⋅5
Cancel the common factor.
z=2⋅12⋅5
Rewrite the expression.
z=15
z=15
z=15
z=15
z=15
The result can be shown in multiple forms.
Exact Form:
z=15
Decimal Form:
z=0.2
Solve for z 4/z=18/(5z)+2

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