Download 4.1 - 4.3 - Interval Notation

Math 096 – Section 4.1
Interval Notation
(1,5)
Inequality
Graph
X7
[-4,5)
0x5
(2,)
X ≤ -1
X≥6
[-2,8]
All real numbers
(-,8]
-1  x  5
[-5, 4)
2) Properties of Inequalities – Due the day we do this section in class
Fill in the blanks with appropriate numbers and inequalities:
7

3
Add 3 to both sides and get
Subtract 8 from both sides
Multiply both sides by 5
Divide both sides by (-1)
Multiply both sides by (- 3)
Divide both sides by 6
The only time we switch the sense of the inequality is when we _____________ or __________ both
sides of the inequality by a ___________ number.
1
3) Solve inequalities algebraically.
a. Linear inequalities
Solve as if you were solving a linear equation
In the last step, when you divide by the coefficient of the variable, switch the inequality
only if you are dividing by a negative number
(1) 3(x – 5) + 2 > 5x - 10
5  2x 2x 1

2
4
(2) Now solve
b. Compound inequalities (section 4.3)
(3) Graph
(4) Solve and graph
(5) Graph
x ≤ -10 or x > 8
3x < -15 or 2x > 22
x ≤ 10 and x > - 8
(6) Solve and graph
2x ≥ -10 and x < 8
(7) Graph
-1 < x < 2
(8) Solve and graph
-15 < 3x – 7 ≤ 8
(9) Now solve for y
1
3 1
 y 
2
2 2
2
Section 4.2 – solving equations graphically
10) Estimate the value of x for which
=
Problem (A)
The solution to the equation is x = ...........
...............
. (It is the x-coordinate of the point of intersection)
Problem (B)
The solution to the equation is x =
11) The graphs of y1 = -2x + 8 and y2 = -4x + 12 are shown.
FIRST: USE THE GRAPH TO Estimate the solution to -2x + 8 = -4x + 12. (it is the x-coordinate of the
point of intersection)
SECOND, use algebra to solve the equation
-2x + 8 = -4x + 12.
12) The graphs of y1 = -x - 4 and y2 = x - 10 are shown.
FIRST: USE THE GRAPH TO Estimate the solution of -x - 4 = x - 10.
SECOND, use algebra to solve the equation
-x - 4 = x - 10
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