Algebra
What is Algebra?
Algebra is a branch of mathematics where we use letters (variables) to represent unknown numbers. Instead of solving "what number plus 4 equals 10?", algebra lets us write it as an equation: n + 4 = 10.
Key Terms
Variable β a letter that represents an unknown value.
x, y, n, a are all variables.
Expression β a combination of numbers, variables, and operations. No equals sign.
3x + 2 Β· 5y - 7 Β· 4aΒ²
Equation β a statement that two expressions are equal. Has an equals sign.
3x + 2 = 11 Β· 5y - 7 = 3
Coefficient β the number multiplied by the variable.
In 4x, the coefficient is 4.
Solving One-Step Equations
The goal is to get the variable alone on one side. Whatever you do to one side, you must do to the other.
x + 5 = 12 Subtract 5 from both sides: x = 12 β 5 = 7
3x = 18 Divide both sides by 3: x = 18 Γ· 3 = 6
Solving Two-Step Equations
Work backwards: undo addition/subtraction first, then multiplication/division.
2x + 4 = 12 Step 1 β subtract 4: 2x = 8 Step 2 β divide by 2: x = 4
5x β 3 = 17 Step 1 β add 3: 5x = 20 Step 2 β divide by 5: x = 4
The Distributive Property
The distributive property lets you expand brackets:
a(b + c) = ab + ac
3(x + 4) = 3x + 12 2(5 β y) = 10 β 2y
Substitution
When you are given the value of a variable, substitute (swap in) the number and calculate.
Find 3x + 2 when x = 5: = 3(5) + 2 = 15 + 2 = 17
Order of Operations (BODMAS)
Always follow this order: Brackets β Orders (powers) β Division β Multiplication β Addition β Subtraction.
2 + 3 Γ 4 = 2 + 12 = 14 (not 20)