A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

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 + 3 < \( \frac{x}{-7} \)
-7 x (4x + 3) < x
(-7 x 4x) + (-7 x 3) < x
-28x - 21 < x
-28x - 21 - x < 0
-28x - x < 21
-29x < 21
x < \( \frac{21}{-29} \)
x < -\(\frac{21}{29}\)

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

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 - 3)
(y x y) + (y x -3) + (3 x y) + (3 x -3)
y² - 3y + 3y - 9
y² - 9

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.