Linear equations and inequalities

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عدد المتطلبات السابقة الإلزامية (حتى الأساس): 9

ستتعلّم

• 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.

تعريف

• 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.

مبرهنة

• 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.

مفاهيم خاطئة شائعة

• 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.

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اكتشافات اختيارية

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

مسارات التعلّم

• Adult beginner pathway

قراءات إضافية

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