Transcript 3.4

M60 Day 12
3.4 Solving Inequalities
Warm-up
1. Solve.
1
1
n6  n5
3
4
2. Scott’s averaging 60 mph on his drive from St. Louis,
MO to Memphis, TN. If the total trip is 285 miles, how
long should he expect the drive to take?
3. Marissa has five exam scores of 75, 82, 90, 85, and 77
in her chemistry class. What score does she need on
the final exam to have an average of 80 (to earn a B –
100 max points for the exam).
Notation
• Finite – elements can be counted
example: {17, 18, 25}
• Infinite – elements cannot be counted
“To infinity and beyond” (Buzz Lightyear, Toy Story)
example: {…-3, -2, -1, 0, 1, 2 , -3…}
Intervals: Types & Notation
Slide 6 in 3.4
Linear Inequalities
• 10 < 15
• 10 - 3 < 15 - 3
• 10(2) < 15(2)
• 10 - 20 < 15 - 20
• All TRUE and the inequality’s “sense” remained
the same … but WAIT there’s more…
Solving Linear Inequalities
Multiplying and dividing both sides of an
inequality by a negative number causes the
“sense” of the inequality to be reversed.
10  15
12  16
10  5  ? 15  5 
12 16
?
4 4
Linear Equation versus Inequality
When solving:
• Linear Equations – generally have one solution
• Linear Inequality – generally have an infinite
number of solutions.
Example #1
• Solve the inequality. Write the solution using
interval notation and then graph the solution
set.
3  2 x  5   3  x  1
Example #2
• Solve the inequality. Write the solution in
algebraic notation and graph the solution set.
3  x  2  4  x  1

2
3
Try it…
• Solve the inequality and graph the solution
set. Write the solution using interval notation.
4  2x  5  x
Compound Inequalities
• Compounds have 3 PARTS…what you do to
one part you have to do to ALL the parts!
• Solve the COMPOUND inequality. Write the
solution using interval notation and graph the
solution set.
2  x  2  6
Compound inequality
• Solve the COMPOUND inequality. Write the
solution using interval notation and graph the
solution set.
2
1  x 1  9
3
Try it…
• Solve the COMPOUND inequality. Write the
solution using interval notation and graph the
solution set.
3  4 x  3  1
Lesson 4.1
Cartesian Coordinates
Cartesian Coordinate System
Graphing
• Create a table of ordered pairs.
• Graph the resulting sets of ordered pairs.
x y 7
Coming up…
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Day 13 Reading Guide
Quiz 5 Due November 8th
Test #2 Due November 15th
Week 7, Hawkes grade adjustment
Exit Ticket
1. Solve the inequality. Write the solution using
interval notation and graph the solution set.
4x  7  9
2. Solve the compound inequality. Write the
solution using interval notation and graph
the solution set.
5  4 x  1  11