1.8 Solving Absolute 1.8 Solving Absolute Value Value

Equations and Equations and InequalitiesInequalities

Objectives: Write, solve, and graph absolute Objectives: Write, solve, and graph absolute value equations and inequalities in mathematical value equations and inequalities in mathematical

and real world situations.and real world situations.

Standards: 2.8.11.A Analyze a given set of data Standards: 2.8.11.A Analyze a given set of data for the existence of a pattern and represent the for the existence of a pattern and represent the

pattern algebraically and graphically.pattern algebraically and graphically.

I. Absolute ValueI. Absolute Value

The absolute value of x is the distance The absolute value of x is the distance

from x to 0 on the number line.from x to 0 on the number line.

-3 -3 = =

5 5 == -256,000 -256,000 ==

3

5

256000

II. Absolute Value EquationsII. Absolute Value Equations

Break up the original absolute Break up the original absolute value equation into 2 value equation into 2 equations. One of the equations. One of the

equations equals the positive equations equals the positive value of the right side and the value of the right side and the

other equation equals the other equation equals the negative value.negative value.

If x = a, then x = a or x = - a.

Solve each absolute value equation. Solve each absolute value equation. Graph the solution on a calculator. Graph the solution on a calculator.

Ex 1. Ex 1. 2x + 3 2x + 3 = 4 check and = 4 check and graphgraph

Ex 1. Ex 1. 2x + 3 2x + 3 = 4= 4

Solve each absolute value equation. Solve each absolute value equation. Graph the solution on a calculator. Graph the solution on a calculator. **

Ex 2. Ex 2. 3x + 5 3x + 5 = 7 Check and = 7 Check and graphgraph

Solve each absolute value equation. Solve each absolute value equation. Graph the solution on a calculator. Graph the solution on a calculator. **

Ex 3. Ex 3. x - 3 x - 3 = 3x + 5= 3x + 5

Check the solutions. Do they work?

Graph the solution(s) on a number line.

Solve each absolute value equation. Solve each absolute value equation. Graph the solution on a calculator. Graph the solution on a calculator. **

Ex 4. Ex 4. x – 4 x – 4 == x + 1x + 1

III. Absolute Value InequalitiesIII. Absolute Value Inequalities How to tell the difference between How to tell the difference between ANDAND and and OROR statements:statements:If If a a > 0 and > 0 and x x < < aa, then , then x x < < aa AND AND xx > > -a.-a.If If a a > 0 and > 0 and x x > > aa, then , then x x > > aa OR OR xx < < -a.-a.

Break the original absolute value inequality into 2Break the original absolute value inequality into 2inequalities. The first inequality is the same as the inequalities. The first inequality is the same as the original problem, but it does not include the absoluteoriginal problem, but it does not include the absolutevalue bars. For the second inequality, flip thevalue bars. For the second inequality, flip theinequality sign and change the sign of the number on inequality sign and change the sign of the number on the right side.the right side.

Solve the absolute value inequality. Solve the absolute value inequality. Graph the solution on a number line.Graph the solution on a number line.

Ex 1. Ex 1. 5 – 3x 5 – 3x < 9< 9

Ex 1. Ex 1. 5 – 3x 5 – 3x < 9< 9

Solve the absolute value inequality. Solve the absolute value inequality. Graph the solution on a number line.Graph the solution on a number line.

1.1. 5x – 3 5x – 3 < 7< 7

2.2. 3x – 7 3x – 7 > 1> 1

3.3. 5x + 2 5x + 2 >> 8 8

HomeworkHomework

Integrated Algebra II- Section 1.8 Level AIntegrated Algebra II- Section 1.8 Level A

Academic Algebra II- Section 1.8 Level BAcademic Algebra II- Section 1.8 Level B