Download Solving Inequalities

Chapter 5
Solving Linear Inequalities
5.1 Solving Inequalities by Addition and
Subtraction
CLE 3102.3.4; SPI 3102.3.5
Solve problems involving linear equations and linear inequalities.; Write and/or
solve linear equations, inequalities, and compound inequalities including those
containing absolute value.
Solve multi-step linear inequalities with one variable and graph the solution on a
CFU3102.3.13; CLE 3102.3.4; number line.; Solve problems involving linear equations and linear inequalities.;
SPI 3102.3.5
Write and/or solve linear equations, inequalities, and compound inequalities
5.2 Solving Inequalities by Multiplication and
including those containing absolute value.
Division
Solve multi-step linear inequalities with one variable and graph the solution on a
number line.; Solve problems involving linear equations and linear inequalities.;
CFU3102.3.13; CLE 3102.3.4; Write and/or solve linear equations, inequalities, and compound inequalities
SPI 3102.3.5; SPI 3102.3.5 including those containing absolute value.; Write and/or solve linear equations,
inequalities, and compound inequalities including those containing absolute
value.
5.3 Solving Multi-Step Inequalities
5.4 Solving Compound Inequalities
5.5 Inequalities Involving Absolute Value
5.6 Graphing Inequalities in Two Variables
SPI 3102.3.5
Write and/or solve linear equations, inequalities, and compound inequalities
including those containing absolute value.
CFU3102.3.14; SPI 3102.3.5
Solve absolute value equations and inequalities (including compound
inequalities) with one variable and graph their solutions on a number line.;
Write and/or solve linear equations, inequalities, and compound inequalities
including those containing absolute value.
Graph linear inequalities on the coordinate plane and identify regions of the
graph containing ordered pairs in the solution.; Solve problems involving linear
CFU3102.3.26; CLE 3102.3.4;
equations and linear inequalities.; Write and/or solve linear equations,
SPI 3102.3.5
inequalities, and compound inequalities including those containing absolute
value.
• Are the number of
students playing volleyball
more or less than the
number in track and field?
• How would you write this
as a mathematical
sentence?
• Suppose 1200 schools
added both sports would
this change the situation? Volleyball < Track & Field
13,426< 14,587
• Can we show this
13,426 +1200 < 14,587+1200
mathematically?
14,626 < 15,287
Inequalities
•<
• Less than
• Fewer than
•>
• Greater than
• More than
•≤
• At most
• No more than
• Less than or equal to
•≥
• At Least
• No less than
• Greater than or equal to
Graphing Inequalities
• Graph t < 5
• Graph t > 5
• Graph t ≤ 5
• Graph t ≥ 5
-5
-5
-5
-5
0
0
5
5
0
0
If variable is < or > graph using an open circle
If variable is ≤ or ≤ graph using a closed circle
5
5
Solving Inequalities
• Solve S – 12 > 65, then Graph on a
number line
1. Determine what answer
will look like
2. Eliminate Grouping
Symbols
3. Eliminate Fractions
4. Add or subtract to isolate
variable
5. Divide by Coefficient
6. Check solution
S – 12 > 65
+12
+12
S > 77
77
Solving Inequalities
• Solve 12 ≥ y - 9 ,
then graph on a number line
1. Determine what answer
will look like
2. Eliminate Grouping
Symbols
3. Eliminate Fractions
4. Add or subtract to isolate
variable
5. Divide by Coefficient
6. Check solution
12 ≥ y - 9
+9
21 ≥ y
21
Solving Inequalities
• Solve 5p + 7 > 6p,
then graph on a number line
1. Determine what answer
will look like
2. Eliminate Grouping
Symbols
3. Eliminate Fractions
4. Add or subtract to isolate
variable
5. Divide by Coefficient
6. Check solution
5p + 7 > 6p
-5p
7>p
p<7
7
-5p
Write an inequality
• Four times a number is no more than three
times that number plus eight.
• 4x  3x + 8
• Seven times a number is greater than six
times that number minus 2.
• 7x > 6x -2
• A number decreased by 8 is at most 14.
• X – 8  14
• A number plus 7 is greater than 2
• X+7>2
Practice
• Page 286 12 - 40, every 4th