How do we solve Absolute Value Inequalities?

How do we solve Absolute Value Inequalities?

Do Now: If we change the sign of an inequality, what do we do with the

sign?

Do Now: If we change the sign of an inequality, what do we do with the

sign?

How is solving absolute value inequalities different from linear

inequalities?

How is solving absolute value inequalities different from linear

inequalities? Once again, we are going to have to set up TWO

equations AFTER we have ISOLATED THE ABSOLUTE VALUE!!!

Once it is ISOLATED, we write the two equations. For the first we just write it as is, dropping the absolute

value. For the second we drop the absolute value but change

the sign of the other side, and flip the inequality!

Once again, we are going to have to set up TWO equations AFTER we have ISOLATED THE ABSOLUTE VALUE!!!

Once it is ISOLATED, we write the two equations. For the first we just write it as is, dropping the absolute

value. For the second we drop the absolute value but change

the sign of the other side, and flip the inequality!

ExampleExample

|x+3|< 5

x+3<5 x+5> –5

x<2 x>-10

|x+3|< 5

x+3<5 x+5> –5

x<2 x>-10

-10 2

Another exampleAnother example

|2x-1| ≥ x+10

2x-1 ≥ x+10 2x-1 ≤ -x-10

x ≥ 11 3x ≤ -9

x ≤ -3

|2x-1| ≥ x+10

2x-1 ≥ x+10 2x-1 ≤ -x-10

x ≥ 11 3x ≤ -9

x ≤ -3-3 11

ExampleExample

The “average” twenty-five-year-old female in the United States measures 5 feet 4 inches.A) If most twenty-five-year-old women measure within 2

inches of this height, us an absolute value inequality to express this fact.

B) Determine the range of heights that satisfy this inequality. Express your answer in feet and inches.

C) Graph the solution on a number line, using inches as your unit of measure.

The “average” twenty-five-year-old female in the United States measures 5 feet 4 inches.A) If most twenty-five-year-old women measure within 2

inches of this height, us an absolute value inequality to express this fact.

B) Determine the range of heights that satisfy this inequality. Express your answer in feet and inches.

C) Graph the solution on a number line, using inches as your unit of measure.

Try on your ownTry on your own

|x-2| > 7|x-2| > 7

Another oneAnother one

When an oven is set to 350º, the temperature, t varies slightly from this setting. When the temperature varies by more than 7º, the oven will turn on (or off) until it reaches 350º again.A) Write an absolute value inequality that will express

this fact.

B) Solve the absolute value inequality to determine when the oven will turn on or off.

C) Graph the solution on a number line.

When an oven is set to 350º, the temperature, t varies slightly from this setting. When the temperature varies by more than 7º, the oven will turn on (or off) until it reaches 350º again.A) Write an absolute value inequality that will express

this fact.

B) Solve the absolute value inequality to determine when the oven will turn on or off.

C) Graph the solution on a number line.

Summary/ HomeworkSummary/ Homework

What do you need to remember to do when you set up the two inequalities?

HW: pg 112, 1-12 even, 13-16 all

What do you need to remember to do when you set up the two inequalities?

HW: pg 112, 1-12 even, 13-16 all