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 = 11a

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.

(4a)(9ab) - (2a²)(5b)
(4 x 9)(a x a x b) - (2 x 5)(a² x b)
(36)(a¹⁺¹ x b) - (10)(a²b)
36a²b - 10a²b
26a²b

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.

-3x + 8 < \( \frac{x}{5} \)
5 x (-3x + 8) < x
(5 x -3x) + (5 x 8) < x
-15x + 40 < x
-15x + 40 - x < 0
-15x - x < -40
-16x < -40
x < \( \frac{-40}{-16} \)
x < 2\(\frac{1}{2}\)

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, \(c = \sqrt{a + b}\)

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).