To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.

8c - 4z = 9c - 5z + 4
8c = 9c - 5z + 4 + 4z
8c - 9c = -5z + 4 + 4z
-c = -z + 4
c = \( \frac{-z + 4}{-1} \)
c = \( \frac{-z}{-1} \) + \( \frac{4}{-1} \)
c = z - 4

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

4b + 2 > \( \frac{b}{5} \)
5 x (4b + 2) > b
(5 x 4b) + (5 x 2) > b
20b + 10 > b
20b + 10 - b > 0
20b - b > -10
19b > -10
b > \( \frac{-10}{19} \)
b > -\(\frac{10}{19}\)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

-2b + 8 = 5 + 8b
-2b = 5 + 8b - 8
-2b - 8b = 5 - 8
-10b = -3
b = \( \frac{-3}{-10} \)
b = \(\frac{3}{10}\)

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y - 3)(y - 2)
(y x y) + (y x -2) + (-3 x y) + (-3 x -2)
y² - 2y - 3y + 6
y² - 5y + 6