Transcript Interval Notation and Inequalities

*
Math 021
*Interval Notation is a way to write a set of real
numbers.
The following are examples of how

sets of numbers can be written in interval
notation:
Graph
Inequality
Interval
2 x 3
(-2, 3]
x3
(-∞, 3)
x  2
[-2, ∞)
x  2 or x  3 (-∞,-2] ∪ (3,∞)
Inequality
a.
b.
c.
d.
x  4
1 x  4
x0
x  1 or x  2
Graph
Interval
*Solving Linear Inequalities
*Solving linear inequalities is similar to solving linear
equations. Replace the inequality with an equal sign
and solve using the same rules as solving linear
equations. When solving, there is a rule of
inequalities that must be followed:
*If a ,b, and c are real numbers and c < 0:
If a < b, then ac > bc
If a > b, then ac < bc
*In other words multiplying or dividing an inequality
by a negative number flips the inequality.
*Examples – Solve, graph, and write
each inequality in interval notation:
*a.
*b.
*c.
*d.
*e.
*f.
3x – 1 < 11
2(x + 3) ≥ x + 4
4(3x – 1) ≤ 10(x + 1)
4x + 15 + x > 3 + 2x + 6
-6x - 2 ≤ 10
30 < -5x
*Solving Compound Inequalities
*A compound inequality is any inequality that
contains two or more inequality symbols.
*A union between two inequalities is all the set
of all elements that belongs to either
inequality.
*Keyword for union is Or
*An intersection of two inequalities is the set of
all elements that belong to both inequalities.
*Keyword for intersection is And
* Examples – Solve, graph, and write each inequality in
interval notation:
* a.
6 < 3x ≤ 15
1
2
c. 2 ≤ x + 3 ≤ 7
b. -6 ≤ 5x – 1 < 9
d. 𝑥 > 5 𝑜𝑟 2𝑥 ≤ −4
e. 2 𝑥 + 3 ≤ 0 𝑜𝑟 𝑥 − 1 ≥ 7
f. 3𝑥 − 1 ≤ 5 𝑜𝑟 − 10𝑥 < 20