An equation is two expressions separated by an equal sign. The key to solving equations is to 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.

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

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.

z + 1 > \( \frac{z}{5} \)
5 x (z + 1) > z
(5 x z) + (5 x 1) > z
5z + 5 > z
5z + 5 - z > 0
5z - z > -5
4z > -5
z > \( \frac{-5}{4} \)
z > -1\(\frac{1}{4}\)

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(5a)(7ab) - (8a²)(5b)
(5 x 7)(a x a x b) - (8 x 5)(a² x b)
(35)(a¹⁺¹ x b) - (40)(a²b)
35a²b - 40a²b
-5a²b