Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

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.

You need to find the value of c so solve the first equation in terms of x:

4c + x = -5
x = -5 - 4c

then substitute the result (-5 - 4c) into the second equation:

5c - 9(-5 - 4c) = 3
5c + (-9 x -5) + (-9 x -4c) = 3
5c + 45 + 36c = 3
5c + 36c = 3 - 45
41c = -42
c = \( \frac{-42}{41} \)
c = -1\(\frac{1}{41}\)

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.

-5z - 1 < 6 - 2z
-5z < 6 - 2z + 1
-5z + 2z < 6 + 1
-3z < 7
z < \( \frac{7}{-3} \)
z < -2\(\frac{1}{3}\)

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)