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
Page 1 of 31
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!!!
Page 2 of 31
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.
Page 3 of 31
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
Page 5 of 31
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- algebra carson dellosa
- chapter 3 linear equations and inequalities
- lecture 5 1 linear programming stanford university
- solving equations with multiple variables worksheet answer key shmoop
- lesson 6 2 6 multi step inequalities with distributive property pc mac
- solving inequalities
- mathematics inequalities in one and two variables georgia standards
- solving one step inequalities multiplying ipa kuta software
- unit 1 review equations and inequalities
- algebra 1 spencer unit 4 notes inequalities and graphing linear
Related searches
- solving inequalities and graphing steps
- graphing linear inequalities pdf
- graphing linear inequalities khan academy
- solving inequalities and graphing worksheet
- graphing linear inequalities calculator
- graphing linear inequalities practice
- graphing linear inequalities in two variables
- algebra 1 solving inequalities worksheet
- algebra 1 graphing inequalities worksheet
- graphing linear inequalities worksheet pdf
- graphing linear inequalities worksheet answers
- algebra 1 graphing worksheet