Math Pacing

1 / 19

# Math Pacing - PowerPoint PPT Presentation

Solving Open Sentences Involving Absolute Value. | | | | | | | | | |. | | | | | | | | | |. – 3 – 2 – 1 0 1 2 3 4 5 6. – 5 – 4 – 3 – 2 – 1 0 1 2 3 4. Math Pacing. Solving Open Sentences Involving Absolute Value. There are three types of open sentences that can involve absolute value.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Math Pacing' - sauda

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Solving Open Sentences Involving Absolute Value

| | | | | | | | | |

| | | | | | | | | |

– 3 – 2 – 1 0 1 2 3 4 5 6

– 5 – 4 – 3 – 2 – 1 0 1 2 3 4

Math Pacing

Solving Open Sentences Involving Absolute Value

There are three types of open sentences that can involve absolute value.

### Solving Open Sentences Involving Absolute Value

Consider the case | x | = n.

| x | = 5 means the distance between 0 and x is 5 units

If | x | = 5, then x = – 5 or x = 5.

The solution set is {– 5, 5}.

Solving Open Sentences Involving Absolute Value

When solving equations that involve absolute value, there are two cases to consider:

### Solving Open Sentences Involving Absolute Value

Case 1 The value inside the absolute value symbols is positive.

Case 2 The value inside the absolute value symbols is negative.

Equations involving absolute value can be solved by graphing them on a number line or by writing them as a compound sentence and solving it.

means that the distance between b and –6 is 5 units. To find b on the number line, start at –6 and move 5 units in either direction.

Solve an Absolute Value Equation

Example 5-1a

Method 1 Graphing

The distance from –6 to –11 is 5 units.

The distance from –6 to –1 is 5 units.

Write as or

Original inequality

Case 1

Case 2

Subtract 6 from eachside.

Simplify.

Solve an Absolute Value Equation

Example 5-1a

Method 2 Compound Sentence

So, an equation is .

Write an Absolute Value Equation

Example 5-2a

Write an equation involving the absolute value for the graph.

Find the point that is the same distance from –4 as the distance from 6. The midpoint between –4 and 6 is 1.

The distance from 1 to –4 is 5 units.

The distance from 1 to 6 is 5 units.

Check Substitute –4 and 6 into

Write an Absolute Value Equation

Example 5-2a

Write an Absolute Value Equation

Example 5-2b

Write an equation involving the absolute value for the graph.

Solving Open Sentences Involving Absolute Value

Consider the case | x | < n.

| x | < 5 means the distance between 0 and x is LESS than 5 units

### Solving Open Sentences Involving Absolute Value

If | x | < 5, then x > – 5 andx < 5.

The solution set is {x| – 5 < x < 5}.

Solving Open Sentences Involving Absolute Value

When solving equations of the form | x | < n, find the intersection of these two cases.

### Solving Open Sentences Involving Absolute Value

Case 1 The value inside the absolute value symbols is less than the positive value of n.

Case 2 The value inside the absolute value symbols is greater than negative value of n.

Then graph the solution set.

Write as and

Case 2

Case 1

Original inequality

Simplify.

Solve an Absolute Value Inequality (<)

Example 5-3a

Then graph the solution set.

Solve an Absolute Value Inequality (<)

Example 5-3b

Solving Open Sentences Involving Absolute Value

Consider the case | x | > n.

| x | > 5 means the distance between 0 and x is GREATER than 5 units

### Solving Open Sentences Involving Absolute Value

If | x | > 5, then x < – 5 orx > 5.

The solution set is {x| x < – 5 or x > 5}.

Solving Open Sentences Involving Absolute Value

When solving equations of the form | x | > n, find the union of these two cases.

### Solving Open Sentences Involving Absolute Value

Case 1 The value inside the absolute value symbols is greater than the positive value of n.

Case 2 The value inside the absolute value symbols is less than negative value of n.

Then graph the solution set.

Write as or

Case 2

Case 1

Original inequality

Simplify.

Divide each side by 3.

Simplify.

Solve an Absolute Value Inequality (>)

Example 5-4a

Solve an Absolute Value Inequality (>)

Example 5-4a

Then graph the solution set.

Solve an Absolute Value Inequality (>)

Example 5-4b

Solving Open Sentences Involving Absolute Value

In general, there are three rules to remember when solving equations and inequalities involving absolute value:

### Solving Open Sentences Involving Absolute Value

• If then or(solution set of two numbers)
• If then and(intersection of inequalities)
• If then or(union of inequalities)