# A.5d and *A.5cd - Systems of Linear Inequalities

A.5    The student will solve multistep linear inequalities in two variables, including

d)  solving systems of inequalities.

A.5  The student will

c)  solve practical problems involving inequalities;

d)  represent the solution to a system of inequalities graphically.

Bloom's Level:  Evaluate

### 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.
• Real-world problems can be modeled and solved using linear inequalities.
• Properties of inequality and order can be used to solve inequalities.
• Set builder notation may be used to represent solution sets of inequalities.

·  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 Multiplication

­   Commutative Property of Multiplication

­  Identity Property of Multiplication (Multiplicative Identity)

­  Inverse Property of Multiplication (Multiplicative Inverse)

­  Distributive Property

·  Properties of Inequality:

­  Transitive Property of Inequality

­  Subtraction Property of Inequality

­  Multiplication Property of Inequality

­  Division Property of Inequality

Substitution

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

A.5d1  Solve systems of linear inequalities algebraically and graphically.

·  A.5cDetermine whether a coordinate pair is a solution of a linear inequality or a system of linear inequalities.

·  A.5dRepresent the solution of a system of two linear inequalities graphically.

·  A.5bdDetermine 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

Updated: Oct 27, 2017