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.

-8y + 4 < 2 + 4y
-8y < 2 + 4y - 4
-8y - 4y < 2 - 4
-12y < -2
y < \( \frac{-2}{-12} \)
y < \(\frac{1}{6}\)

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

5a(a - z)
5(7)(7 + 5)
5(7)(12)
(35)(12)
420

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.

(6a)(2ab) - (5a²)(2b)
(6 x 2)(a x a x b) - (5 x 2)(a² x b)
(12)(a¹⁺¹ x b) - (10)(a²b)
12a²b - 10a²b
2a²b

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°).

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 -42 as well and sum (Inside, Outside) to equal -1. For this problem, those two numbers are -7 and 6. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - y - 42
y² + (-7 + 6)y + (-7 x 6)
(y - 7)(y + 6)