When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

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 - 1)
(y x y) + (y x -1) + (-3 x y) + (-3 x -1)
y² - y - 3y + 3
y² - 4y + 3

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

3a + 7a = 10a

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.

4x - 4 < \( \frac{x}{-5} \)
-5 x (4x - 4) < x
(-5 x 4x) + (-5 x -4) < x
-20x + 20 < x
-20x + 20 - x < 0
-20x - x < -20
-21x < -20
x < \( \frac{-20}{-21} \)
x < \(\frac{20}{21}\)