Algebra 1 – Spencer – Unit 4 Notes: Inequalities and Graphing Linear ...

Algebra 1 ? Spencer ? Unit 4 Notes: Inequalities and Graphing Linear Equations

Unit Calendar

Date Nov 5 (A )

Topic 6.1 Solving Linear Inequalities +/6.2 Solving Linear Inequalities x/? 6.3 Solving Multi-step Linear Inequalities

Nov 9 (A) Nov 11 (A)

Quiz on Inequalities 4.1 Coordinate Plane Warm Up 4.2 Graph Linear Equations 4.4. Finding Slope and Rate of Change 4.5 Graph Using Slope-Intercept Form

Nov 13 (A) Nov 17 (A)

Nov 19 (A) Nov 23 (A)

Quiz on 4.1, 4.2, 4.4, 4.5 4.3 Graph Using Intercepts 4.6 Model Direct Variation 4.7 Graph Linear Functions

Review/Exploration Unit 4 Test

Homework

6.1-6.3 HW worksheet (drilling holes/crossword puzzle)

4.2 Worksheet (ketchup)

4.4-4.5 Worksheet (don't feel well/A duck that steals/swallowed the silver dollar) 4.3 Worksheet (purpose of HW/did you hear about) 4.6-4.7 Worksheet (Grok jumping/grafun/poor man drink coffee)

Vocabulary: inequality, equivalent inequalities, solution of an inequality, quadrant, standard rom, linear function, x-intercept, y-intercept, slope, rate of change, slopeintercept form, parallel, direct variation, constant of variation, parent linear function

SOLs: A.5 A.7

A.8

The student will solve multistep linear inequalities in two variables, including b) justifying steps used in solving inequalities, using axioms of inequality and

properties of order that are valid for the set of real numbers and its subsets; c) solving real-world problems involving inequalities.

The student will investigate and analyze function (linear) families and their characteristics both algebraically and graphically, including d) x- and y-intercepts; f) making connections between and among multiple representations of functions

including concrete, verbal, numeric, graphic, and algebraic.

The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

Textbook reference: Chapter 6, sections 1-3, Chapter 4

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Algebra 1 ? Spencer ? Unit 4 Notes: Inequalities and Graphing Linear Equations Introduction to Inequalities

An inequality is a mathematical sentence that uses an inequality symbol to compare the values of two expressions. The word inequality means not equal.

The table shows some of the meanings for the inequality symbols.

<

>

is less than is greater than is less than or equal to is greater than or equal

is fewer than is more than is no more than

to

exceeds

is at most

is no less than

is at least

Verbal Phrase

Inequality Graph

All real numbers less than 2

All real numbers greater than -2

All real numbers less than or equal to 1 All real numbers greater than or equal to 0 ***When you just want greater than or less than, you use a

on the graph.

***When you want equal to as well as greater than or less than, you use

Try these:

1. x > 3

2. x < -1

3. x 2

4. x 0

STOP

What if an equation is not quite ready to graph? You already know how to get a variable by itself . . . that is just what you'll do here!!

Example: x + 3 < 10 -3 -3

Undo the added 3 by subtracting 3 from both sides

x < 7

Easy!!!

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Algebra 1 ? Spencer ? Unit 4 Notes: Inequalities and Graphing Linear Equations

Another example:

5 Easy!!

5x > 20 5x > 20 55

x > 4

Undo the multiplied 5 by dividing both sides by

Practice: More than 15,000 fans, f, attended the football game last night.

Examples: Solve and check. y + 5 > 11

-21 > d ? 8

Solve and graph on a number line. c ? (-2) < 3

y < n -2 A number, n, decreased by 7 is at most 23.

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Algebra 1 ? Spencer ? Unit 4 Notes: Inequalities and Graphing Linear Equations

** Multiplication and Division Properties of Equality introduce a new concept. **

THE FLIPPER RULE

When multiplying or dividing by a negative number, flip the inequality symbol.

So, when you multiply or divide both sides by a negative number, just flip the inequality!!

Watch:

-3x > 15

Check:

- 3x -3

>

15 - 3

x < - 5

As soon as I divide by the negative number, I circle the inequality to remind me to change it on the next line!!

Check:

x < -2 - 4

-4? x 1 -4

<

x > 8

-2(-4) When I multiplied both sides by -4, I circled 12

2.

x 30 5

3. ?6x 26

4. x ? 2 < -5

5.

x 10 - 4

6. 3x -21

Solving Multi-Step Inequalities Multi-step inequalities are solved in the same way that one-step inequalities are solved. We use the properties of inequality to transform the original inequality into a series of simpler, equivalent inequalities.

1) Simplify each side of the inequality 2) Add or subtract ? Addition or Subtraction Properties of Inequality 3) Multiply or divide to isolate the variable ? Multiplication or Division Properties of

Inequality (Remember FLIPPER!!) 4) Check by substitution Examples: Solve and graph. 5 + 13 > 83

2( + 3) < -4

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