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

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 + 4 < \( \frac{x}{6} \)
6 x (3x + 4) < x
(6 x 3x) + (6 x 4) < x
18x + 24 < x
18x + 24 - x < 0
18x - x < -24
17x < -24
x < \( \frac{-24}{17} \)
x < -1\(\frac{7}{17}\)

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(8²) + 2π(8 x 5)
sa = 2π(64) + 2π(40)
sa = (2 x 64)π + (2 x 40)π
sa = 128π + 80π
sa = 208π

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.

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 equal sign and the answer on the other.

-4a + 9 = \( \frac{a}{4} \)
4 x (-4a + 9) = a
(4 x -4a) + (4 x 9) = a
-16a + 36 = a
-16a + 36 - a = 0
-16a - a = -36
-17a = -36
a = \( \frac{-36}{-17} \)
a = 2\(\frac{2}{17}\)