quick algebra questions?

First question: Solve -2(x + 2) + 5 = 6 + 4(1 - x)

-2(x + 2) + 5 = 6 + 4(1 - x)

-2x - 4 + 5 = 6 + 4 - 4x

-2x + 1 = 10 - 4x

2x + 1 = 10

2x = 9

x = 4.5

2nd Question: To find the slop and y-intercept, you need to get the equation into the y=mx+b form.

-4x + 5y = 10

5y = 4x + 10

y = (4/5)x + 2

slope = 4/5, y-intercept = +2

3rd Question: find f^-1(x)

First, realize that "y" and "f(x)" mean exactly the same think. It is like saying you want to buy 12 donuts or buy a dozen donuts. The two symbols are identically interchangeable with each other.

f(x) = -4x - 2

rewrite using "y" instead of "f(x)"

y = -4x - 2

To find the inverse, simply exchange the "y" and "x" terms. Wherever there is a "y", put an "x". And wherever there is an "x", put a "y". Yes, it looks weird, but it really is that easy.

x = -4y - 2

Now just re-solve the equation for "y=....."

4y + x = -2

4y = -x - 2

y = (-1/4)x - (1/2)

That is the inverse!