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Solving and Graphing Linear Inequalities

- Solving One-Step Linear Inequalities

Whats an inequality?

- Is a range of values,
- rather than ONE set number
- An algebraic relation showing that a quantity is

greater than or less than another quantity. - Speed limit

Symbols

Less than

Greater than

Less than OR EQUAL TO

Greater than OR EQUAL TO

Solutions.

You can have a range of answers

All real numbers less than 2 xlt 2

Solutions continued

All real numbers greater than -2

x gt -2

Solutions continued.

All real numbers less than or equal to 1

Solutions continued

All real numbers greater than or equal to -3

Did you notice,

Some of the dots were solid and some were open?

Why do you think that is?

If the symbol is gt or lt then dot is open because

it can not be equal. If the symbol is ? or ? then

the dot is solid, because it can be that point

too.

Write and Graph a Linear Inequality

Sue ran a 2-K race in 8 minutes. Write an

inequality to describe the average speeds of

runners who were faster than Sue. Graph the

inequality.

Faster average speed gt

Solving an Inequality

Solving a linear inequality in one variable is

much like solving a linear equation in one

variable. Isolate the variable on one side using

inverse operations.

Solve using addition

x 3 lt 5

Add the same number to EACH side.

x lt 8

Solving Using Subtraction

Subtract the same number from EACH side.

Using Subtraction

Graph the solution.

Using Addition

Graph the solution.

THE TRAP..

When you multiply or divide each side of an

inequality by a negative number, you must reverse

the inequality symbol to maintain a true

statement.

Solving using Multiplication

Multiply each side by the same positive number.

Solving Using Division

Divide each side by the same positive number.

Solving by multiplication of a negative

Multiply each side by the same negative number

and REVERSE the inequality symbol.

Multiply by (-1).

Solving by dividing by a negative

Divide each side by the same negative number and

reverse the inequality symbol.

Homework

Page 337 338 22-54 evens 55-60 61

65

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