Algebra 1
Every lesson explains the concept, works through examples, and gives you practice problems with full solutions. Work through them in order, or jump to the topic you need.
24 lessons
- How to Solve One-Step EquationsSolve one-step equations by doing the same inverse operation to both sides, with worked examples, common mistakes, and practice problems with full solutions.
- How to Solve One-Step InequalitiesSolve one-step inequalities the same way as equations, plus the one rule that changes: why the sign flips when you multiply or divide by a negative.
- How to Solve Two-Step EquationsSolve two-step equations by undoing addition first and multiplication second, with worked examples, common mistakes, and practice problems with full solutions.
- How to Solve Multi-Step EquationsSolve multi-step equations by distributing, combining like terms, then undoing operations in reverse order, with worked examples and practice problems.
- How to Solve Multi-Step InequalitiesSolve multi-step inequalities by distributing, combining like terms, and undoing operations in reverse order, including when to flip the inequality sign.
- What Slope Is, and Why It Never Changes on a LineLearn what slope measures, how to find it with rise over run and the slope formula, and why similar triangles guarantee it is the same everywhere on a line.
- Slope-Intercept Form: y = mx + bUnderstand y = mx + b, what m and b each control, how to graph a line from it in two moves, and how to rewrite any linear equation into this form.
- Solving Equations with Variables on Both SidesSolve equations with variables on both sides by collecting variable terms on one side, plus how to recognise no solution and infinitely many solutions.
- How to Solve Compound Inequalities (AND and OR)Solve compound inequalities joined by AND or OR, graph the solution on a number line, and tell which combinations give no solution or every number.
- How to Graph Linear EquationsGraph a line three ways — from slope-intercept form, from intercepts, or from a table — and understand why every point on the line is a solution.
- How to Solve Literal Equations and Rearrange FormulasRearrange a formula to solve for any variable using the same inverse operations you use on numbers, with worked examples from geometry, physics, and finance.
- Point-Slope Form: Writing a Line from One PointLearn point-slope form, why it is the slope formula rearranged, and how to use it to write a line's equation from a single point and a slope.
- Solving Quadratic Equations by FactoringSolve quadratics by factoring using the zero product property, why the equation must equal zero first, and how to factor the common trinomial patterns.
- How to Write the Equation of a Line from Two PointsFind a line's equation from any two points: compute the slope, substitute into point-slope form, then simplify — with worked examples and full solutions.
- x-Intercepts and y-Intercepts: Finding Where a Line CrossesFind the x- and y-intercepts of any equation by setting the other variable to zero, why that works, and what intercepts mean in a real situation.
- How to Solve Absolute Value EquationsSolve absolute value equations by splitting into two cases, why two answers appear, when there is no solution, and how absolute value inequalities differ.
- Completing the Square, Step by StepLearn completing the square: why the method works geometrically, how to handle a leading coefficient, and how it produces vertex form and the quadratic formula.
- Parallel and Perpendicular Lines: The Slope RulesParallel lines have equal slopes and perpendicular lines have negative reciprocal slopes — why both rules are true, and how to write equations using them.
- The Quadratic Formula: How and Why It WorksLearn the quadratic formula, where it comes from, and how to use it to solve any quadratic equation, with worked examples and practice problems.
- Standard Form of a Linear Equation: Ax + By = CWhat standard form is, when it beats slope-intercept form, how to convert between the two, and how to find the slope without rearranging.
- Function Notation: What f(x) Actually MeansUnderstand f(x) as a name and an input rather than multiplication, how to evaluate it, and how to read statements like f(3) = 7 in context.
- Domain and Range: The Inputs and Outputs of a FunctionWhat domain and range mean, how to find them from a graph, a table or an equation, and why some inputs have to be excluded.
- Rate of Change: Slope With Units AttachedWhat average rate of change means, how it relates to slope, how to compute it from a table or a function, and how to read its units and sign.
- Linear vs Nonlinear Functions: How to Tell Them ApartFour reliable tests for deciding whether a relationship is linear — from its equation, its table, its graph, or its rate of change.