➗ Algebra Refresher

What you’ll learn

1. Variables and ExpressionsUnderstand variables, coefficients, constants and how to evaluate expressions.A variable is a letter standing for a number, and an expression like 3x + 7 combines coefficients, variables and constants. Evaluating means substituting a value and simplifying, which generalises arithmetic to statements true for every number.
2. Order of OperationsApply the order of operations correctly.When operations mix, PEMDAS sets the order: parentheses, exponents, multiplication/division, then addition/subtraction, each left to right. The convention guarantees every expression has a single agreed value.
3. Solving Linear EquationsSolve linear equations by keeping both sides balanced.An equation is a balance; you isolate the variable by undoing operations in reverse, doing the same to both sides. Removing constants first and then the coefficient uncovers the solution, which you confirm by substituting back.
4. Negatives and FractionsWork confidently with negative numbers and fractions.Negatives extend the number line left of zero, and sign rules make like signs multiply positive and unlike signs negative. Fractions mean division, and a fractional coefficient is cleared by multiplying both sides by its reciprocal.
5. Exponents and PowersUse exponents and the basic power rules.An exponent is repeated multiplication, and the core rules add exponents to multiply like bases, subtract to divide, and multiply for a power of a power. Because each step multiplies, exponents produce explosive growth.
6. PolynomialsIdentify polynomial parts, combine like terms and distribute.A polynomial sums terms of coefficients times powers of a variable; only like terms (same variable and power) can be combined. The distributive law a(b+c)=ab+ac expands products and clears parentheses.
7. FactoringFactor common factors and simple quadratics, and see why it matters.Factoring reverses distribution, first by pulling out a common factor, then for a quadratic by finding two numbers that multiply to the constant and add to the middle coefficient. Factoring reveals zeros via the zero-product property, which solves equations.
8. Lines and SlopeGraph and interpret lines in slope-intercept form.A linear equation graphs as y = mx + b, where m is the slope (rise over run) and b is the y-intercept. The sign and size of m tell whether the line rises, falls or is flat, and how steep it is.
9. Systems of EquationsSolve systems of linear equations by substitution and elimination.A system is solved where its lines cross — the (x, y) satisfying both equations. Substitution puts one equation into the other, while elimination adds or subtracts to cancel a variable; both reduce the system to one unknown.
10. Formulas and Word ProblemsRearrange formulas and translate word problems into equations.Formulas are equations you can rearrange with the same balancing rules to solve for any quantity. Modelling a word problem means naming the unknown, translating the words into an equation, solving, and interpreting the result.

Questions this course answers

Grounded in trusted sources

• OpenStax — 'Elementary Algebra' and 'Intermediate Algebra' (openstax.org)
• Khan Academy — Algebra 1 (khanacademy.org)
• OpenStax — 'Prealgebra'

Every Wunder lesson is built from real, reputable sources — never invented.

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