#### Math - 2018-19

# AII.3a - Abs Value Equations/Inequalities

AII.3The student willsolvea) absolute value linear equations and inequalities;

*Adopted: 2016*

### 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

·
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.3a_{1} **Solve**
absolute value linear equations or inequalities in one variable
algebraically.

·
AII.3_{1} **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*