Math - 2018-19
A.5cd - Systems of Linear Inequalities
A.5 The student will
c) solve practical problems involving inequalities;
d) represent the solution to a system of inequalities graphically.
BIG IDEAS
- I can set a freezer
temperature so ice cubes won’t melt, make sure a bridge will hold a loaded
truck, determine how many hours I’d have to work to afford the shoes I want,
avoid receiving a speeding ticket when I can drive, and won’t go over the
allowed number of text messages per month on my cell phone.
- I will apply algebraic properties
and processes to model real-life situations, remembering that the solution will
be a range of possibilities, and absolute value inequalities are used for situations
where margin of error is a concern.
UNDERSTANDING THE STANDARD
· A solution to an inequality is the value or set of values that can be substituted to make the inequality true.
· The graph of the solutions of a linear inequality is a half-plane bounded by the graph of its related linear equation. Points on the boundary are included unless the inequality contains only < or > (no equality condition).
· Practical problems may be modeled and solved using linear inequalities.
· Solutions and intervals may be expressed in different formats, including set notation or using equations and inequalities.
- Examples may include:
Equation/ Inequality |
Set Notation |
x = 3 |
{3} |
x = 3 or x = 5 |
{3, 5} |
y≥ 3 |
{y: y ≥ 3} |
Empty (null) set ∅ |
{ } |
· Properties of Real Numbers and Properties of Inequality are applied to solve inequalities.
· Properties of Real Numbers:
Associative Property of Addition
Associative Property of Multiplication
Commutative Property of Addition
Commutative Property of Multiplication
Identity Property of Addition (Additive Identity)
Identity Property of Multiplication (Multiplicative Identity)
Inverse Property of Addition (Additive Inverse)
Inverse Property of Multiplication (Multiplicative Inverse)
Distributive Property
· Properties of Inequality:
Transitive Property of Inequality
Addition Property of Inequality
Subtraction Property of Inequality
Multiplication Property of Inequality
Division Property of Inequality
SubstitutionESSENTIALS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
·
A.5c_{2 }Determine
whether a coordinate pair is a solution of a linear inequality or a system of
linear inequalities.
· A.5d_{1 }Represent the solution of a system of two linear inequalities graphically.
· A.5bd_{1 }Determine and verify algebraic solutions using a graphing utility.
KEY VOCABULARY
inequality, axiom, properties of order,
properties of inequality, solution set, systems of linear inequalities set
builder notation