Transcript Lesson 1.7A Notes

Warm-up – pick up handout up front
1.
Solve by factoring. Answers:
1000x3-10x
1.x=0, x=1/10, x= -1/10
Solve for x
2.
2.
3x  2  4  4
HW 1.7A (2-14 evens, 21-24, 39-47)
2
 
3
HW 1.6B (31-39 all)
HW 1.6C (61-75 odds)
31.x  4 32.x  9 33. x  13 34. x  -1
35.x  5 4 36.x  5 27 37. x  68 38. x  3
39.x  5and  4
61.x  8and  8 63. x  9and  5 65. x  3and  2
5
2
2
4
67.x  3and  69. x  and  71. x   and 4
3
5
5
5
1
73. no solution 75. x 
2
Lesson 1.7A Solving linear
inequalities and the types of
notation
 Objective: To be able to use interval notation
when solving linear inequalities, recognize
inequalities with no solution or all real
numbers as a solution.
The set of all solutions is called the solution set
of the inequality. Set-builder notation and a
new notation called interval notation, are used
to represent solution sets. (See Handout!)
Interval Notation: See Handout
Example 1:
(-1,4]
Graph and write the solution in set-builder notation.
(
]
-1
0
Interval Notation
(-1,4] =
4
Set Builder Notation
{x -1 < x ≤ 4}
The answer is read x such that -1 is
less than x which is less than or equal to 4.
You Try: (-∞, -4)
)
-4
(-∞, -4) = { x
x < -4}
0
Graphing intervals on a number line!
Example 2:
Graph each interval on a number line.
(2,3]
(
]
2
3
Write answer using set builder
notation.
{x 2 < x < 3}

You try: Graph and
write in set builder notation.
[1,6)
[
)
1
6
(-3,7]
(
-3
]
7
{x
1 < x < 6}
{x
-3 < x < 7}
Example 3: Solve and graph this linear
inequality.
-2x - 4 > x + 5
Remember to switch the
sign when you multiply or
divide by a negative.
x < -3
)
-3
0
You Try!!
 3x+1 > 7x – 15
 Use interval notation to express the solution set.
 Graph the solution.
Answer: (-∞, 4)
)
4
Inequalities with Unusual Solution
Sets
Some inequalities have no solution.
Example 4: x > x+1
There is no number that is greater than itself
plus one.
The solution set is an empty set ( this is a
zero with a slash through it)

Notes Continued:
Like wise some inequalities are true for all
real numbers such as:
Example 5: x<x+1.
Every real number is less than itself plus 1.
The solution set is { x x is a real number}
Interval notation, ( , ) or all real
numbers.
Notes Continued:
When solving an inequality with no
solution, the variable is eliminated
and there will be a false solution such
as 0 > 1.
When solving an inequality that is all
real numbers, the variable is
eliminated and there will be a true
solution such as 0 < 1.
Example 6:
Solving a linear inequality for a solution set.
 A. 2 (x + 4) > 2x + 3
 B. x + 7 < x – 2
solution: 7 < -2
solution: 8 > 3
The inequality 8>3 is true
for all values of x. The
solution set is
{x
x is a real number} or
 ,  
The inequality 7 < -2 is
false for all values of
x. The solution set is

You try: 3(x + 1) > 3x + 2
3x + 3 > 3x + 2
3 > 2
The solution set is all
real numbers. (-∞,∞)
 Summary: Describe the ways in which solving
a linear inequality is different from solving a
linear equation.