Algebra

Cheat Sheet  ·  Sec 2 Math
Esmeralda Oliversen
KEY VOCABULARY
Variable
letter for unknown (x, y, n)
Coefficient
number × variable: 5x → 5
Like terms
same variable & exponent
Expression
terms combined (no = sign)
Equation
expression = expression
DISTRIBUTIVE LAW
Rule
a(b + c) = ab + ac
3(2x − 5) = 6x − 15
−2(x + 4) = −2x − 8
⚠ −4(x − 2) = −4x + 8 not −4x − 8
Two negatives = positive!
COMBINING LIKE TERMS
5x + 3y − 2x + 7 − y
= (5x−2x) + (3y−y) + 7
= 3x + 2y + 7
SOLVING EQUATIONS — STEPS
  • 1. Expand brackets
  • 2. Move variable terms to one side
  • 3. Move constants to other side
  • 4. Divide by coefficient
  • 5. Substitute back to check!
EQUATION EXAMPLES
3(x−2) = 2x + 7
3x − 6 = 2x + 7
x = 13
x/3 + 1 = x/2 − 2 (LCD=6)
2x + 6 = 3x − 12
x = 18
FRACTION EQUATIONS
  • Find LCD of all denominators
  • Multiply every term by LCD
  • Solve the resulting equation
INEQUALITIES
< >
strict (open circle on line)
≤ ≥
inclusive (closed circle)
⚠ KEY RULE: When multiplying or dividing by a negative number, FLIP the inequality sign!

−3x < 9 → x > −3
INEQUALITY EXAMPLE
5 − 3x ≥ 14
−3x ≥ 9
x ≤ −3  (flipped ÷ by −3)
GRAPHING ON NUMBER LINE
  • x > 3: open circle at 3, arrow right
  • x ≤ −2: closed circle at −2, arrow left
  • Open circle = not included
  • Closed circle = included
WORD PROBLEM METHOD
  • 1. Identify the unknown
  • 2. Let x = the unknown
  • 3. Write the equation
  • 4. Solve
  • 5. Answer with units in a sentence
"A number + 8 = 3× that number − 4"
x + 8 = 3x − 4
12 = 2x → x = 6
COMMON MISTAKES
  • 3(x+2) ≠ 3x+2 — multiply ALL terms
  • Moving terms: sign changes across =
  • Flip inequality when ÷ by negative
  • 3x + 2y ≠ 5xy — unlike terms!
  • Always check by substituting back