Intermediate Algebra Help?

Question

-2a = -4 + x divided by x - 3

How do you solve for x

Answer 1

First, multiply through by x-3, keep in mind x can't be equal to 3 because of the denominator

-2a(x-3) = x-4
Then distribute the 2a

-2ax +6a = x-4

Group terms with the x on one side and other on other side

-2ax -x = -6a -4

factor out x

x(-2a -1) = -6a -4

divide by (-2a -1)

x = (-6a-4)/(-2a-1)

There is a negative sign that can be taken out so

x = (6a+4)/(2a +1)

Answer 2

I intepret your problem statement as follows as shown below. In your problem statement, it was not clear what was divided by x-3

-2a = - 4 + x/(x-3) Add 2a to each side and "flip the equation

x/(x-3) +2a - 4 = 0 Multiply each side by (x-3)

x +2a(x-3) -4(x-3) = 0 Clear the parens

x + 2ax -6a -4x +12 = 0 Combine terms

-3x + 2ax -6a +12 = 0 Multiply by -1

3x -2ax +6a -12 = 0 then factoring

x(3-2a) +6a -12 = 0 Divide by (3-2a)

x + (6a - 12)/(3-2a) = 0

x = -(6a - 12)/(3-2a), or

x = (12-6a)/(3-2a)

Answer 3

-2a = (-4 + x)/(x - 3)
-2a(x - 3) = -4 + x
-2ax + 6a = -4 + x
-2ax - x = -4 - 6a
(-2a - 1)x = -4 - 6a
x = (-4 - 6a)/(-2a - 1)
x = (4 + 6a)/(2a + 1)

Answer 4

You have 2 variables in your question - a and x. You can't solve for x if you don't know a.