6.5 & 6.6 Solving more advanced equations/inequalities

6.5 & 6.6 Isolating the absolute value bars

Let's remind ourselves how to solve first

• Where is the variable: left, right or both sides?

• Look to add or subtract a constant.

• Look to divide or multiply by the number attached to the variable.

What are the steps here to solve?

• Variable is on the left side.

• Subtract 2 from both sides

• Divide by 3 on both sides.

What are the steps here to solve?

• Variable is on the right side.

• Nothing to add or subtract.

• Divide by 2 on each side.

What are the steps here to solve?

• Subtract 2.

• Divide by -3

What are the steps here to solve?

• Add 3.

• Divide by 5.

Open Ended

What are the steps to solve the following inequality?

x - 5 < 6

Open Ended

What are the steps to solve the following equation?

1 = x + 6

Open Ended

What are the steps to solve the following inequality?

28 > 14 + x

Open Ended

What are the steps to solve the following equation?

2x - 5 = 61

Open Ended

What are the steps to solve the following equation?

8 = 2x - 8

Open Ended

What are the steps to solve the following inequality?

6 - 2x > 12

Open Ended

What are the steps to solve the following equation?

5x - 3 = 19

Open Ended

What are the steps to solve the following equation?

2x = 90

Open Ended

What are the steps to solve the following inequality?

17 > 3 + 2x

What's different about solving absolute value inequalities/equations when the bars aren't ISOLATED?

What does it mean to be isolated?

What does it mean to be isolated?

• By yourself

• Alone

• "Quarantined"

Let's talk about what it means to be isolated in math.

• Our goal is usually to isolate the variable.

• But what if the variable is stuck inside absolute value bars??

• Then we need to isolate the bars FIRST!!

Multiple Choice

Are the bars isolated?

2|x+1|< 12

• no

• yes

Multiple Choice

Are the bars isolated?

|x - 1| - 12 = 24

• no

• yes

Multiple Choice

Are the bars isolated?

|x + 2| > 12

• no

• yes

Multiple Choice

Are the bars isolated?

|x| + 4 = 13

• no

• yes

Multiple Choice

Are the bars isolated?

|x + 3| > 41

• no

• yes

Let's talk about the setup

• You've got the values inside the bars.

• And you've got TWO "guards" outside the bars.

• You'll have to add/subtract one guard.

• And you'll have to divide/multiply the other guard,

What are the steps to isolate the bars?

• Subtract 5.

• Divide by 3.

• Now the bars are isolated!

What are the steps to isolate the bars?

• Subtract 5.

• Now the bars are isolated!

What are the steps to isolate the bars?

• Divide by 3.

• Now the bars are isolated!

Open Ended

What are the steps to isolate the bars?

12 |x + 2| - 1 < 4

Open Ended

What are the steps to isolate the bars?

2 |x+1| + 4 = 5

Open Ended

What are the steps to isolate the bars?

|x - 4| + 9 = 18

Open Ended

What are the steps to isolate the bars?

-2|x + 3| = 20

Open Ended

What are the steps to isolate the bars?

3|x - 4| < 21

Open Ended

What are the steps to isolate the bars?

|x + 4| - 9 = 0

Open Ended

What are the steps to isolate the bars?

2 |x| - 1 = 10

Multiple Choice

Which step would you do first?

2|x - 4| < 12

• subtract 2

• divide by 2

• add 4

Multiple Choice

Which step would you do first?

2|x| - 3 = 12

• distribute

• add 3

Multiple Choice

Which step would you do first?

-2|x + 1| + 9 = -34

• add 2

• subtract 9

• add 34

Multiple Choice

Which step would you do first?

-2|x + 1| + 9 = -34

• add 2

• subtract 9

• add 34