Download presentation
1
Chapter 5 Notes Algebra Concepts
2
Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Inequality – Addition Property of Inequalities Words: Symbols:
3
Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Inequality – A mathematical sentence that contains < , > , < , or > Addition Property of Inequalities Words: Any number is allowed to be added to both sides of a true inequality Symbols: If a > b, then a + c > b + c If a < b, then a + c < b + c
4
Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Graphing inequalities on a number line: Put a circle on the _____________ point Fill the circle in if the sign is _______ or _______ Leave the circle open if the sign is _____ or ____ Shade the left side if the variable is ____________ to the number Shade the right side if the variable is ____________ to the number Ex) Graph x < Ex) Graph 4 < x
5
Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Solve the following inequalities and graph the solution set on a number line. 1) x – 12 > 8 2) 22 > x – 8 3) x – 14 < -19
6
Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Subtraction Property of Inequalities Words: Symbols:
7
Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Subtraction Property of Inequalities Words: Any number is allowed to be subtracted from both sides of a true inequality Symbols: If a > b, then a – c > b – c If a < b, then a – c < b – c
8
Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Solve the following inequalities and graph the solution set on a number line. 1) x + 19 > 56 2) 18 > x + 8 3) 22 + x < 5
9
Section 5-1: Solving Linear Inequalities by Addition and Subtraction
Solve the following inequalities and graph the solution set on a number line. 1) 3x + 6 < 4x 2) 10x < 9n – 1
10
Section 5-2: Solving Inequalities by Multiplication and Division
Multiplication Property of Inequalities: Part 1 Words: Symbols:
11
Section 5-2: Solving Inequalities by Multiplication and Division
Multiplication Property of Inequalities: Part 1 Words: Any positive number is allowed to be multiplied to both sides of an inequality Symbols (c > 0): If a > b, then ac > bc If a < b, then ac < bc
12
Section 5-2: Solving Inequalities by Multiplication and Division
Multiplication Property of Inequalities: Part 2 Words: Symbols:
13
Section 5-2: Solving Inequalities by Multiplication and Division
Multiplication Property of Inequalities: Part 2 Words: Any negative number is allowed to be multiplied to both sides of an inequality, as long as the sign gets flipped! Symbols (c < 0): If a > b, then ac < bc If a < b, then ac > bc
14
Section 5-2: Solving Inequalities by Multiplication and Division
Solve 1) 2) 3) 4)
15
Section 5-2: Solving Inequalities by Multiplication and Division
Division Property of Inequalities: Part 1 Words: Any positive number is allowed to be divided to both sides of an inequality Symbols (c > 0): If a > b, then If a < b, then
16
Section 5-2: Solving Inequalities by Multiplication and Division
Division Property of Inequalities: Part 2 Words: Any negative number is allowed to be divided to both sides of an inequality, as long as the sign gets flipped! Symbols (c < 0): If a > b, then If a < b, then
17
Section 5-2: Solving Inequalities by Multiplication and Division
Solve and graph the solution set 1) 4x > 16 2) -7x < 147 3) -15 < 5x 4) -20 > -10x
18
Section 5-3: Solving Multi-Step Inequalities
Solve the following multi-step inequalities. Graph the solution set. 1) -11x – 13 > 42 2) x < 31 3) 23 > 10 – 2x
19
Section 5-3: Solving Multi-Step Inequalities
Solve the following multi-step inequalities. Graph the solution set. 4(3x – 5) + 7 > 8x + 3 2(x + 6) > -3(8 – x)
20
Section 5-3: Solving Multi-Step Inequalities
Translate the verbal phrase into an expression and solve Five minus 6 times a number n is more than four times the number plus 45
21
Section 5-3: Solving Multi-Step Inequalities, SPECIAL SOLUTIONS
Solve the following inequalities. Indicate if there are no solutions or all real number solutions. 1) 9x – 5(x – 5) < 4(x – 3) 2) 3(4x + 6) < (2x – 4)
22
Section 5-6: Graphing Linear Inequalities
Linear Equations vs. Linear Inequalities Plot any 2 points Draw a solid line through the 2 points Put in slope-int form first Plot any two points Determine whether to connect the points with a solid OR dashed line Shade ONE side of the line You must determine which side You shade the solution set!
23
Section 5-6: Graphing Linear Inequalities
Steps for graphing linear inequalities: Plot 2 points on the line If the symbol is < or > connect with a dashed line If the symbol is < or >, connect with a solid line Shade above the line for y > mx + b (or >) 5) Shade below the line for y < mx + b (or <) Ex. Graph y < 2x – 4
24
Section 5-6: Graphing Linear Inequalities
Graph the following linear inequalities Ex) Ex) y < x – 1
25
Section 5-6: Graphing Linear Inequalities
Graph the following linear inequalities Ex) 3x – y < 2 Ex) x + 5y < 10
Similar presentations
© 2024 SlidePlayer.com Inc.
All rights reserved.