-100(0.19x-y)=-100⋅-28.8

The standard form of a linear equation is Ax+By=C.

Multiply by 100100 to remove the decimal.

-100(100⋅0.19100x-y)=-100⋅-28.8

Multiply 100 by 0.19.

-100(19100x-y)=-100⋅-28.8

Cancel the common factor of 19 and 100.

Rewrite 19 as 1(19).

-100(1(19)100x-y)=-100⋅-28.8

Cancel the common factors.

Rewrite 100 as 1(100).

-100(1⋅191⋅100x-y)=-100⋅-28.8

Cancel the common factor.

-100(1⋅191⋅100x-y)=-100⋅-28.8

Rewrite the expression.

-100(19100x-y)=-100⋅-28.8

-100(19100x-y)=-100⋅-28.8

-100(19100x-y)=-100⋅-28.8

-100(19100x-y)=-100⋅-28.8

Multiply by 1010 to remove the decimal.

-100(19100x-y)=-100⋅10⋅-28.810

Multiply 10 by -28.8.

-100(19100x-y)=-100⋅-28810

Move the negative in front of the fraction.

-100(19100x-y)=-100⋅(-28810)

Cancel the common factor of 288 and 10.

Factor 2 out of 288.

-100(19100x-y)=-100⋅(-2(144)10)

Cancel the common factors.

Factor 2 out of 10.

-100(19100x-y)=-100⋅(-2⋅1442⋅5)

Cancel the common factor.

-100(19100x-y)=-100⋅(-2⋅1442⋅5)

Rewrite the expression.

-100(19100x-y)=-100⋅(-1445)

-100(19100x-y)=-100⋅(-1445)

-100(19100x-y)=-100⋅(-1445)

-100(19100x-y)=-100⋅(-1445)

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

100,5

Since 100,5 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 100,5 then find LCM for the variable part .

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 prime factors for 100 are 2⋅2⋅5⋅5.

100 has factors of 2 and 50.

2⋅50

50 has factors of 2 and 25.

2⋅2⋅25

25 has factors of 5 and 5.

2⋅2⋅5⋅5

2⋅2⋅5⋅5

Since 5 has no factors besides 1 and 5.

5 is a prime number

The LCM of 100,5 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2⋅2⋅5⋅5

The LCM of 100,5 is 2⋅2⋅5⋅5=100.

Multiply 2 by 2.

4⋅5⋅5

Multiply 4 by 5.

20⋅5

Multiply 20 by 5.

100

100

100

Multiply both sides by 100.

100(-100(19100x-y))=100(-100⋅(-1445))

Combine 19100 and x.

100(-100(19×100-y))=100(-100⋅(-1445))

Apply the distributive property.

100(-10019×100-100(-y))=100(-100⋅(-1445))

Cancel the common factor of 100.

Factor 100 out of -100.

100(100(-1)19×100-100(-y))=100(-100⋅(-1445))

Cancel the common factor.

100(100⋅-119×100-100(-y))=100(-100⋅(-1445))

Rewrite the expression.

100(-1(19x)-100(-y))=100(-100⋅(-1445))

100(-1(19x)-100(-y))=100(-100⋅(-1445))

Multiply.

Multiply 19 by -1.

100(-19x-100(-y))=100(-100⋅(-1445))

Multiply -1 by -100.

100(-19x+100y)=100(-100⋅(-1445))

100(-19x+100y)=100(-100⋅(-1445))

Apply the distributive property.

100(-19x)+100(100y)=100(-100⋅(-1445))

Multiply.

Multiply -19 by 100.

-1900x+100(100y)=100(-100⋅(-1445))

Multiply 100 by 100.

-1900x+10000y=100(-100⋅(-1445))

-1900x+10000y=100(-100⋅(-1445))

-1900x+10000y=100(-100⋅(-1445))

Cancel the common factor of 5.

Move the leading negative in -1445 into the numerator.

-1900x+10000y=100(-100⋅-1445)

Factor 5 out of -100.

-1900x+10000y=100(5(-20)⋅-1445)

Cancel the common factor.

-1900x+10000y=100(5⋅-20⋅-1445)

Rewrite the expression.

-1900x+10000y=100(-20⋅-144)

-1900x+10000y=100(-20⋅-144)

Multiply.

Multiply -20 by -144.

-1900x+10000y=100⋅2880

Multiply 100 by 2880.

-1900x+10000y=288000

-1900x+10000y=288000

-1900x+10000y=288000

Rewrite the equation with the sides flipped.

288000=-1900x+10000y

Add 1900x to both sides of the equation.

288000+1900x=10000y

Subtract 10000y from both sides of the equation.

288000+1900x-10000y=0

Move 288000.

1900x-10000y+288000=0

1900x-10000y+288000=0

Subtract 288000 from both sides of the equation.

1900x-10000y=-288000

Rewrite in Standard Form -100(0.19x-y)=-100*-28.8