Math - 2017-18

A.5abc and *A.5ac - Linear Inequalities

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

a)  solving multistep linear inequalities algebraically and graphically;

b)  justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets;

c)  solving real-world problems involving 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; 


Bloom's Level:  Evaluate

Adopted: 2009

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.

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 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

  Substitution

ESSENTIALS

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

A.5a1  Solve multi-step linear inequalities in one variable

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

A.5b1  Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers

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

A.5c1  Solve real-world problems involving inequalities.

·  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: Oct 27, 2017