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.

-2c + 1 > -1 - 3c
-2c > -1 - 3c - 1
-2c + 3c > -1 - 1
c > -2

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 5cm + 13cm + 14cm = 32cm

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

x² - 13x + 41 = x - 4
x² - 13x + 41 + 4 = x
x² - 13x - x + 45 = 0
x² - 14x + 45 = 0

Next, factor the quadratic equation:

x² - 14x + 45 = 0
(x - 5)(x - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 5) or (x - 9) must equal zero:

If (x - 5) = 0, x must equal 5
If (x - 9) = 0, x must equal 9

So the solution is that x = 5 or 9

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

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 21 as well and sum (Inside, Outside) to equal 10. For this problem, those two numbers are 3 and 7. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 10y + 21
y² + (3 + 7)y + (3 x 7)
(y + 3)(y + 7)