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.

(8a)(2ab) - (3a²)(2b)
(8 x 2)(a x a x b) - (3 x 2)(a² x b)
(16)(a¹⁺¹ x b) - (6)(a²b)
16a²b - 6a²b
10a²b

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.

3y + 9 < \( \frac{y}{-2} \)
-2 x (3y + 9) < y
(-2 x 3y) + (-2 x 9) < y
-6y - 18 < y
-6y - 18 - y < 0
-6y - y < 18
-7y < 18
y < \( \frac{18}{-7} \)
y < -2\(\frac{4}{7}\)

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 8 x 8 = \( \frac{64}{2} \) = 32

A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with c° = 15, the value of z° is 15.