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.

-3y - 1 < \( \frac{y}{2} \)
2 x (-3y - 1) < y
(2 x -3y) + (2 x -1) < y
-6y - 2 < y
-6y - 2 - y < 0
-6y - y < 2
-7y < 2
y < \( \frac{2}{-7} \)
y < -\(\frac{2}{7}\)

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 -63 as well and sum (Inside, Outside) to equal -2. For this problem, those two numbers are -9 and 7. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 2y - 63
y² + (-9 + 7)y + (-9 x 7)
(y - 9)(y + 7)

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 7)(y + 2)
(y x y) + (y x 2) + (7 x y) + (7 x 2)
y² + 2y + 7y + 14
y² + 9y + 14