The document summarizes key concepts from the first chapter of a Pre-Calculus textbook. It introduces interval notation and defines common inequality symbols like greater than, less than, greater than or equal to, and less than or equal to. It provides examples of writing inequalities using interval notation, such as x > 3 representing the interval (3, ∞).

1. Pre-Calculus
Chapter 1
Fundamentals
Deuteronomy 31:6 Be strong and courageous. Do not fear
or be in dread of them, for it is the LORD your God who goes
with you. He will not leave you or forsake you.”

2. Fundamentals
Interval Notation
&
Inequalities

3. Interval Notation

4. Interval Notation
x>3

5. Interval Notation
x>3 ( 3,∞ )

6. Interval Notation
x>3 ( 3,∞ )
x≥3

7. Interval Notation
x>3 ( 3,∞ )
x≥3 [ 3,∞ )

8. Interval Notation
x>3 ( 3,∞ )
x≥3 [ 3,∞ )
x<5

9. Interval Notation
x>3 ( 3,∞ )
x≥3 [ 3,∞ )
x<5 ( −∞,5 )

10. Interval Notation
x>3 ( 3,∞ )
x≥3 [ 3,∞ )
x<5 ( −∞,5 )
x≤5

11. Interval Notation
x>3 ( 3,∞ )
x≥3 [ 3,∞ )
x<5 ( −∞,5 )
x≤5 ( −∞,5 ]

12. Interval Notation

13. Interval Notation
−3 ≤ x < 4

14. Interval Notation
−3 ≤ x < 4 [ −3, 4 )

15. Interval Notation
−3 ≤ x < 4 [ −3, 4 )
{ x : x ≤ −3 or x > 7}

16. Interval Notation
−3 ≤ x < 4 [ −3, 4 )
{ x : x ≤ −3 or x > 7} ( −∞,−3] U ( 7,∞ )

17. Interval Notation
−3 ≤ x < 4 [ −3, 4 )
{ x : x ≤ −3 or x > 7} ( −∞,−3] U ( 7,∞ )
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“We must believe that we are gifted for something, and that
one thing, at whatever cost, must be attained.”
Marie Curie