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.

8a - 5 < \( \frac{a}{-5} \)
-5 x (8a - 5) < a
(-5 x 8a) + (-5 x -5) < a
-40a + 25 < a
-40a + 25 - a < 0
-40a - a < -25
-41a < -25
a < \( \frac{-25}{-41} \)
a < \(\frac{25}{41}\)

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 -6 as well and sum (Inside, Outside) to equal -1. For this problem, those two numbers are -3 and 2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - y - 6
y² + (-3 + 2)y + (-3 x 2)
(y - 3)(y + 2)

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

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

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(9a)(8ab) + (4a²)(7b)
(9 x 8)(a x a x b) + (4 x 7)(a² x b)
(72)(a¹⁺¹ x b) + (28)(a²b)
72a²b + 28a²b
100a²b