65v=110-32v

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

5v,10,2v

Since 5v,10,2v contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 5,10,2 then find LCM for the variable part v1,v1.

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.

Since 5 has no factors besides 1 and 5.

5 is a prime number

10 has factors of 2 and 5.

2⋅5

Since 2 has no factors besides 1 and 2.

2 is a prime number

The LCM of 5,10,2 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2⋅5

Multiply 2 by 5.

10

The factor for v1 is v itself.

v1=v

v occurs 1 time.

The LCM of v1,v1 is the result of multiplying all prime factors the greatest number of times they occur in either term.

v

The LCM for 5v,10,2v is the numeric part 10 multiplied by the variable part.

10v

10v

Multiply each term in 65v=110-32v by 10v in order to remove all the denominators from the equation.

65v⋅(10v)=110⋅(10v)-32v⋅(10v)

Simplify 65v⋅(10v).

Rewrite using the commutative property of multiplication.

1065vv=110⋅(10v)-32v⋅(10v)

Cancel the common factor of 5.

Factor 5 out of 10.

5(2)65vv=110⋅(10v)-32v⋅(10v)

Factor 5 out of 5v.

5(2)65(v)v=110⋅(10v)-32v⋅(10v)

Cancel the common factor.

5⋅265vv=110⋅(10v)-32v⋅(10v)

Rewrite the expression.

26vv=110⋅(10v)-32v⋅(10v)

26vv=110⋅(10v)-32v⋅(10v)

Combine 2 and 6v.

2⋅6vv=110⋅(10v)-32v⋅(10v)

Multiply 2 by 6.

12vv=110⋅(10v)-32v⋅(10v)

Cancel the common factor of v.

Cancel the common factor.

12vv=110⋅(10v)-32v⋅(10v)

Rewrite the expression.

12=110⋅(10v)-32v⋅(10v)

12=110⋅(10v)-32v⋅(10v)

12=110⋅(10v)-32v⋅(10v)

Simplify each term.

Cancel the common factor of 10.

Factor 10 out of 10v.

12=110⋅(10(v))-32v⋅(10v)

Cancel the common factor.

12=110⋅(10v)-32v⋅(10v)

Rewrite the expression.

12=v-32v⋅(10v)

12=v-32v⋅(10v)

Cancel the common factor of 2v.

Move the leading negative in -32v into the numerator.

12=v+-32v⋅(10v)

Factor 2v out of 10v.

12=v+-32v⋅(2v(5))

Cancel the common factor.

12=v+-32v⋅(2v⋅5)

Rewrite the expression.

12=v-3⋅5

12=v-3⋅5

Multiply -3 by 5.

12=v-15

12=v-15

12=v-15

Rewrite the equation as v-15=12.

v-15=12

Move all terms not containing v to the right side of the equation.

Add 15 to both sides of the equation.

v=12+15

Add 12 and 15.

v=27

v=27

v=27

Solve for v 6/(5v)=1/10-3/(2v)