How do you reduce an equation with multiple variables?

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Quandaries & Queries

Question from Jonathon, a student:

Hi,
How do you reduce an equation with multiple variables?

For example, if 3x + y = k(x-3), what would x be equal to?

Hi Jonathon,

The subject line of you email was "Solving for x" so I expect the task was to solve for x. I am going to look at a slightly different expression.

4kx - 5z = z(x + 3)

First expand the right side and then collect the terms involving x on the left and all the remaining terms on the left.

4kx - 5z = z(x + 3)
4kx - 5z = zx + 3z
4kx - zx = 3z + 5z
(4k - z)x = 8z
x = 8z/(4k - z)

Penny

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