# AII.3a - Abs Value Equations/Inequalities

AII.3  The student will solve

a)  absolute value linear equations and inequalities;

### BIG IDEAS

• I can find how far and how fast a bus travels, the number and combinations of fruits that can be purchased, and how long it takes to drain a swimming pool.
• I will be able to write symbolic representations of the way numbers behave and will know that in order to maintain equality, an operation performed on one side must also be performed on the other side.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - AII.3 Understanding

·  The definition of absolute value (for any real numbers a and b, where

b  0, if |a|= b, then a = b or a = − b) is used in solving absolute value equations and inequalities.

·  Absolute value inequalities in one variable can be solved algebraically using a compound statement.

### ESSENTIALS

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

·  AII.3a1  Solve absolute value linear equations or inequalities in one variable algebraically.

·  AII.31  Solve equations and verify algebraic solutions using a graphing utility.

### KEY VOCABULARY

absolute value equations, absolute value inequalities, quadratic equation, complex numbers, rational algebraic expression, radical expression, algebraically, graphically, quadratic function, discriminant, real solutions, complex solutions, monomial, binomial, denominator, quadratic formula, verify, completing the square

Updated: Aug 23, 2018