1.8 Number Lines 1.9 Opposites and Absolute Values Warm – up: State the numbers that would represent the following: – A gain of 24 yards – A loss of a down – Lending $50 (as the borrower) – Lending $50 (as the lender) Tell whether the following statements are true or false. 2 < 5 4 < 0 -3 > -2 8 > < < Objective: To graph real numbers on a number line and compare real numbers and to use opposites and absolute values.

1.8 Number Lines What are integers? – Positive Integers {1, 2, 3, 4, 5, …} What are those curly brackets?!? – Negative Integers {-1, -2, -3, -4, -5, …} – Integers {…, -3, -2, -1, 0, 1, 2, 3, …} Whole Numbers – Consist of just the Positive Integers and Zero {0, 1, 2, 3, 4, 5, …} Real Numbers – Consist of any number that we can find on the number line

1.8 Number Lines Write a number to represent each situation. Then write the opposite of that situation and write a number to represent it. Eight steps up Two miles west A wage decrease of $ miles north

1.8 Number Lines What are the four different inequalities? ><≤≥ Translate into symbols: Negative 3 is greater than negative 33. State two inequalities for the coordinates of the points shown below: Complete using to make a true statement. -5 ___ -4 ½ _____ ¼ -10_____ 0.1

1.8 Number Lines 1.9 Opposites and Absolute Values Translate each statement into symbols. Negative eleven is less than negative one. Ten is greater than seven. Zero is greater than negative three tenths. What is the opposite of: (5 + 4) -(8 + 9) -(-10) a If a is positive, then –a is ______________.

1.9 Opposites and Absolute Values Opposites What is the opposite of: (5 + 4) -(8 + 9) -(-10) a If a is positive, then –a is ______________. Absolute Values If a is positive, |a| = a. If a is negative, |a| = -a. If a is zero, |a| = 0. |-4| + |7| |7 – 4| |4 – 7| -[-|-4|] -(12 – 12)

1.9 Opposites and Absolute Values More Absolute Values Write an inequality to make the statement true. -(-2) ____ |-3| |-15| _____|-6| -3 _____ -|-3| Evaluate if t = -4: |t| -t + 9 Solve for x. |x| = 88 |x| = 12.9 |x| = -5 |x| = 0

1.9 Opposites and Absolute Values True or False? The absolute value of a number is always positive. A number and its absolute value can never be equal. If b is a negative number, then the opposite of b is also negative. Homework: – Pg. 34 Written Exercises #15 – 22, 39 – 46 – Pg. 38 Written Exercises # odd Challenge Problems: #