Linear equations and inequalities

Se basa en

Requisitos previos obligatorios, hasta el fondo: 9

Aprenderás a

• 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.

Definición

• 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.

Teorema

• 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.

Errores frecuentes

• 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.

Conduce a

Descubrimientos opcionales

• Linear algebra Systems of many linear equations in many unknowns are the starting point of linear algebra.

Itinerarios de aprendizaje

• Adult beginner pathway

Lecturas complementarias

• I. M. Gelfand and A. Shen, Algebra (1993)