# A.5ac - Linear Inequalities

A.5  The student will

a)  solve multistep linear inequalities in one variable algebraically and represent the solution graphically;

c)  solve practical problems involving inequalities;

### 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

2016 VDOE Curriculum Framework - AI.5 Understanding

·  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.5aSolve multistep linear inequalities in one variable algebraically and represent the solution graphically.

·  A.5aApply the properties of real numbers and properties of inequality to solve multistep linear inequalities in one variable algebraically.

·  A.5cSolve practical problems involving linear inequalities.

·  A.5acDetermine 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: Aug 23, 2018