Help.ai Learn · Skill guide

Linear equations

Solve a one-variable linear equation with justified steps. Keep both sides equal and check the solution in the original relationship.

Read the guide See a worked example

What you’ll learn

Recognize an equation as a statement of equality.
Use operations that preserve its solutions.
Verify a proposed solution by substitution.

An equation states a relationship

Solving asks which value makes the statement true. A linear equation has the variable to the first power after simplification; begin by identifying the variable and what the expressions mean.

Preserve equality at each step

Apply the same addition or subtraction to both sides, or multiply or divide both sides by the same nonzero number. Explain the operation rather than treating a sign change as unexplained movement across the equals sign.

A mistake to avoid

Dividing only one term on a side changes the equation. Keep grouped expressions together, and substitute into the original equation rather than checking only the final rearranged line.

Worked example

Solve 3x + 5 = 20

Subtract 5 from both sides to obtain 3x = 15. Divide both sides by 3 to get x = 5. Substitution confirms 3 × 5 + 5 = 20.

Learning paths that include this skill

Choose the route that fits your goal. The same skill can be useful in more than one subject or stage of learning.

Preparing for algebraPre-algebraConnect arithmetic to algebra through signed numbers, fractions, proportions, equations, and graphs. Review the specific foundation that blocks the next step.Signed numbers · Equivalent fractions · Decimals · Proportions · +6 more Secondary / high-school algebraHigh-school algebraWork through the relationships behind secondary algebra. Reuse number skills, connect equations to graphs, and build toward systems and quadratics.Signed numbers · Equivalent fractions · Decimals · Linear equations · +4 more Secondary geometry and trigonometryGeometry & trigonometryConnect measurement and geometric reasoning to triangle ratios and the unit circle. Keep the meaning of each angle, length, and coordinate visible.Shapes & angles · Area & volume · Linear equations · Geometric reasoning & proofs · +4 more Preparing for calculusPrecalculus foundationsReview equation, graph, and angle foundations before calculus. Identify the prerequisite that needs attention and connect formal notation to its meaning.Linear equations · Systems of equations · Quadratic equations · Graphs & coordinates · +5 more Introductory linear algebraLinear algebra foundationsBuild from equations and coordinates to vectors and matrices. Explain what each component represents and how a matrix-vector calculation combines quantities.Signed numbers · Graphs & coordinates · Linear equations · Systems of equations · +2 more Goal-led refresherAdult math refresherRefresh the mathematics behind a real task, from a percentage or measurement to an equation or graph. Use familiar goals and revisit only the skills you need.Place value · Addition & subtraction · Multiplication · Long division · +12 more

Systems of equationsSolve two linear equations together using their shared variables. Connect elimination or substitution to the intersection of the corresponding relationships.Quadratic equationsRecognize a quadratic equation and connect its roots to factors or a graph. Work through a factorable example and check every proposed solution.Graphs & coordinatesRead a graph as a relationship between quantities. Check axes and scale, connect points to an equation, and interpret the change between two points.

A question worth talking through.

Explore the AI Tutor we’re developing for clear explanations, useful follow-up questions, and guided practice.

Explore AI Tutor