lecture recording on 02 September 2025 at 14.25.04 PM

Instructor highlights class performance (10/10s, 8/10s, 9/10s) and acknowledges some students are refreshing math skills for General Chemistry.
Office hours: Tuesdays 4:00–5:00 PM; Wednesdays 10:00 AM–12:00 PM (as stated in transcript). Also tutoring services available through department and math/science resources.
How to access help: tutoring, learning labs, and a ‘request a tutor’ option in the right-hand gold block for the semester.
Emphasis on securing a tutor early in the semester rather than waiting until late.
Technical issue noted: a student reports smart work showing as overdue despite completion; instructor offers to check.
Today’s plan: focus on algebra skills and solving equations for a single variable, then simplify and solve algorithmic expressions.
Next class (Thursday): quiz on this material, including the topics of scientific notation and significant figures from the previous class.
Friday due: smart work assignment covering scientific notation, significant figures, and today’s algebra.
If you have trouble accessing SmartWork: inform instructor or TA for assistance.
Visual and practice resources mentioned: Moodle modules (balance-scale visualization) and a hands-on whiteboard activity for the first four worksheet questions.
A quick note on class logistics: students will use whiteboards; reference to a module that uses a balance metaphor for solving equations.
The instructor expresses willingness to work more on topics during office hours if needed.

By the end of the lecture, you should be able to:
- Apply algebraic rules to solve equations for a single variable.
- Simplify and solve algorithmic expressions.
- Use a balance metaphor (visualization) to understand solving steps.
- Recognize and apply algebraic properties and rules (to be covered below).

Central principle: whatever is done to one side of an equation must be done to the other side.
This creates a balance between variable terms and constant terms on both sides of the equation.
Practical takeaway: do one operation at a time on one side, then mirror that operation on the other side to preserve equality.
Example setup described in lecture (conceptual): isolate a single variable (e.g., x) by applying the same operation to both sides and moving non-x terms away from the side containing x.
Visualization cue: module on Moodle uses a balance scale to walk through problems step-by-step.

Given an equation (context from lecture): apply distribution, collect like terms, and isolate x.
Step 1: Distribute a factor into parentheses if present (e.g., distribute 2 into (x + 6)).
- Resulting idea: place all x terms on one side and constants on the other as you manipulate.
Step 2: Get all non-x terms off the side with x (e.g., subtract 9 from both sides, if present).
Step 3: Collect like x terms on one side (e.g., move 4x terms to the other side by subtraction).
Step 4: Solve for x by dividing by the coefficient of x (e.g., divide both sides by -3 to isolate x).
Demonstrated result (from transcript): after a sequence of steps, you can arrive at a solution such as x = 1.
Reflection prompt: if any doubt remains, use Moodle module visualization or a whiteboard to walk through the problem.

Moodle module provides a balance-scale visualization to practice solving problems.
In-class activity uses whiteboards for the first four worksheet questions to reinforce the process.

Commutative Property
- Addition: a + b = b + a
- Multiplication: a × b = b × a
- Note: Commutative properties do not apply to subtraction or division (e.g., a − b ≠ b − a; a ÷ b ≠ b ÷ a in general).
Associative Property
- Addition: (a + b) + c = a + (b + c)
- Multiplication: (a × b) × c = a × (b × c)
Distributive Property
- a(b + c) = ab + ac
FOIL (First, Outer, Inner, Last) for multiplication of binomials
- (A + B)(C + D) = AC + AD + BC + BD
- FOIL helps ensure every term inside parentheses is distributed.
Note on FOIL: FOIL is a practical mnemonic for distributing when multiplying binomials; always check that every term is accounted for in the expansion.

The next set of problems focuses on distributing algebraic expressions and solving using those distributions.
The instructor suggests working with whiteboards to practice and mentions you can skip the top-right problem for now if you want a challenge later.
Example discussion points from problems in the sheet:
- Solve x + 3 = -12; and other distribution-related variants.
- In problems with two variables (e.g., x and y), isolate the x-variable by removing terms that don’t contain x on the side with x, then rearrange to isolate x.
- When a second variable is present, you may end up with an expression like x = something that involves y, e.g., x = (-27 - 12y) / 6.
Conceptual check: foiling and distribution rules help verify that each term has been accounted for in expansions.

When an unknown appears in both x^2 and x (a quadratic in standard form), you can use the quadratic formula:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Steps to apply:
- Put the equation in standard form $a x^2 + b x + c = 0.$ If needed, move terms to one side to achieve this form.
- Identify coefficients a, b, c.