Grades 6–8AlgebraPlanned
Linear equations and inequalities
Solving linear equations and inequalities in one variable by doing the same thing to both sides, checking solutions, and modelling word problems.
math.algebra.linear-equations
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
Builds on
Required prerequisites, all the way down: 9
You will learn to
- Solve linear equations with the variable on both sides, including fractions and negative coefficients.
- Recognise equations with exactly one solution, no solution or infinitely many solutions.
- Solve linear inequalities, reversing the inequality when multiplying or dividing by a negative number.
Definition
- A linear equation in x is one that can be written as ax + b = cx + d.
- A solution is a value of the variable that makes the equation true.
- Two equations are equivalent if they have the same solutions.
Theorem
- Adding the same number to both sides, or multiplying both sides by the same non-zero number, gives an equivalent equation.
- ax = b has exactly one solution if a ≠ 0, none if a = 0 and b ≠ 0, and every number as a solution if a = b = 0.
- Multiplying both sides of an inequality by a negative number reverses its direction.
Common misconceptions
- Multiplying both sides by zero, or by an expression that might be zero, and expecting an equivalent equation.
- Forgetting to reverse an inequality after multiplying by a negative number.
- Applying an operation to only one term on a side of the equation.
Leads to
Optional discoveries
- Linear algebra Systems of many linear equations in many unknowns are the starting point of linear algebra.
Learning pathways
Further reading
- I. M. Gelfand and A. Shen, Algebra (1993)