Linear equations

Solve linear equations with equal operations on both sides and check the original conditions.

Meaning

A linear equation simplifies to with Isolate the unknown by undoing addition with subtraction and multiplication by a nonzero number with division. Applying the same inverse operation to both sides preserves equality and can be reversed, so it preserves the solutions.

Example

In subtract 4 to undo the 4 added to the term containing x. Subtracting 4 from both sides gives Divide both sides by 3 to turn three times x into one x, giving Substitution checks in the original equation.Moving a term across the equals sign abbreviates adding or subtracting the same quantity on both sides. A divisor must be nonzero, and any values excluded by the original denominators remain excluded.

Practice for this concept

Scope and references

Topics

Transposing terms, simplifying coefficients, brackets, fractional and decimal coefficients

Learning goal

Solve linear equations with equal operations on both sides and check the original conditions.

Helpful background

Revisit equality and the distributive law only as needed for the equation.

Linear-equation practice

Does not cover fractional or decimal coefficients or every application.

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