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.

(9a)(8ab) - (6a²)(6b)
(9 x 8)(a x a x b) - (6 x 6)(a² x b)
(72)(a¹⁺¹ x b) - (36)(a²b)
72a²b - 36a²b
36a²b

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.

y - 5 < \( \frac{y}{6} \)
6 x (y - 5) < y
(6 x y) + (6 x -5) < y
6y - 30 < y
6y - 30 - y < 0
6y - y < 30
5y < 30
y < \( \frac{30}{5} \)
y < 6

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.

-4a - 5 < 7 + 7a
-4a < 7 + 7a + 5
-4a - 7a < 7 + 5
-11a < 12
a < \( \frac{12}{-11} \)
a < -1\(\frac{1}{11}\)

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.

6a - 5a = 1a

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.