Welcome to Your December Cycle Preview

After consulting with your math teachers, I have gathered a collection of high-impact resources to help you prepare for the upcoming curriculum. Getting a head start on these topics isn't just about "looking smart" in class—it is about building deep confidence in your problem-solving abilities so that when the lectures begin, you are already familiar with the logic behind the math.

Below, you will find a breakdown of the three major pillars for this cycle: Literal Equations, Absolute Value Equations, and Inequalities. Each section includes a brief overview of the concept and a link to a curated YouTube playlist that you can watch anytime, anywhere.

1. Solving Equations for a Variable (Literal Equations)

In this unit, you will move beyond solving for a single number and start solving for specific variables within formulas. This is often called working with Literal Equations. The goal is to isolate a specific variable using inverse operations, exactly as you would with standard numbers.

Key Concept:

  • Treat all other variables as if they were constants (numbers).
  • Reverse the order of operations (PEMDAS) to isolate your target.

For example, if you need to solve for $t$ in the distance formula:

$$d = rt$$

You simply divide both sides by $r$:

$$t = \frac{d}{r}$$

Watch the playlist below to master manipulating formulas:

▶ Watch: Solving Equations for a Variable Playlist

2. Solving Absolute Value Problems

Absolute value represents the distance a number is from zero on a number line. Because distance is always non-negative, absolute value equations often result in two possible solutions (or "cases").

The Two Cases Rule:
When solving an equation like $|x| = a$ (where $a > 0$), you must split the equation into two separate scenarios:

  1. Case 1: $x = a$
  2. Case 2: $x = -a$

For example, to solve $|x - 2| = 5$, you would set up:

$$x - 2 = 5 \quad \text{and} \quad x - 2 = -5$$

Be careful! If an absolute value is set equal to a negative number (e.g., $|x| = -3$), there is no solution, because distance cannot be negative.

▶ Watch: Solving Absolute Value Problems Playlist

3. Solving Inequalities

Solving inequalities is very similar to solving standard equations, with one crucial difference regarding multiplication and division.

The Golden Rule of Inequalities:
Whenever you multiply or divide both sides of an inequality by a negative number, you must flip the direction of the inequality symbol.

For instance:

$$-2x > 8$$

When you divide by $-2$, the greater-than sign ($>$) becomes a less-than sign ($<$):

$$x < -4$$

This unit will also cover how to represent these solutions on a number line using open circles ($<, >$) and closed circles ($\leq, \geq$).

▶ Watch: Solving Inequalities Playlist

Take some time to explore these videos. Even watching just one or two from each playlist will give you a significant advantage in the coming weeks. Good luck, and happy solving!