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.

-c - 9 > -8 - 5c
-c > -8 - 5c + 9
-c + 5c > -8 + 9
4c > 1
c > \( \frac{1}{4} \)
c > \(\frac{1}{4}\)

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -27 as well and sum (Inside, Outside) to equal 6. For this problem, those two numbers are -3 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 6y - 27
y² + (-3 + 9)y + (-3 x 9)
(y - 3)(y + 9)

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

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.

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 4² + 8²
c² = 16 + 64
c² = 80
c = \( \sqrt{80} \)