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Mathematics for Economists
Chapter 3
Equations: Rules and terminology
Equivalent equations and inequalities
Equations, terminology
Equations, constants and variables
Classification of equations
Solving equations
Quadratic equations
Reduced quadratic equations
Quadratic equations
Factoring a reduced quadratic expression and completing the square
Factoring a quadratic expression and completing the square
Single equations: Problems
Problem: Solve linear and quadratic equations
Problem: Understanding the quadratic formula
Problem: Solve linear and nonlinear equations
Problem: Simplify by factoring
Problem: Solve equations
Problem: Factor expressions
Problem: Solve inequalities
Problem: Solve text-equations
Problem: Solve equations containing constants
Problem: Solve equations containing constants
Problem: Solve quadratic equations
Problem: Solve quadratic equations
Problem Solve quadratic text-equations
Problem: Solve equations containing square roots
Systems of linear equations
Systems of equations
Problem: Solve systems of equations
Problem: Solve systems of equations
Problem: Solve systems of equations
Problem: Solve non-linear equations
Sums and the summation sign
Summation sign
Summation rules
Problem: Evaluate sums
Problem: Calculate sum
Problem: True or false for sums
Problem: Sums involving the mean
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Equivalent equations and inequalities
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Summary
\(a=b⟺\)
\(a+c=b+c\)
\(a=b⟺\)
\(a-c=b-c\)
\(a=b⟺\)
\(a⋅c=b⋅c\)
(
\(c≠0\)
)
\(a=b⟺\)
\(a/c=b/c\)
(
\(c≠0\)
)
\(a≤b⟺\)
\(a+c≤b+c\)
\(a≤b⟺\)
\(a⋅c≤b⋅c\)
(
\(c>0\)
)
\(a≤b⟺\)
\(a⋅c≥b⋅c\)
(
\(c<0\)
)