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hendricks_beginning_algebra_1e_ch1_3

6 Chapter 1 Real Numbers and Algebraic Expressions located to the right of 0 and negative numbers are located to the left of 0. 0 is neither positive nor negative. Negative Numbers Positive Numbers –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 ���������������������� Graphing or Plotting Real Numbers on a Number Line Step 1: If the number is not an integer, approximate its value to two decimal places. Step 2: Place a dot on its position on the number line. Make the dot easy to distinguish from the number line itself. �� ������������������������ ������������������ Graph each number on a real number line. 2a. 5 2b. -3 2c. 2 3 2d. -4 1 2 2e. 6.1 2f. 12 Solutions 2a. 5 Graph at the appropriate tick mark. 2b. -3 Graph at the appropriate tick mark. 2c. 2 3 ≈ 0.67 Graph this value between 0 and 1 but closer to 1. 2d. -4 1 2 =-4.50 Graph this value exactly halfway between -4 and -5. 2e. 6.1 Graph this value between 6 and 7 but closer to 6. 2f. 12 ≈ 1.41 Graph this value close to halfway between 1 and 2. –3 √−2 5 6.1 23 –4 1 2 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 Student Check 2 Graph each number on a real number line. a. -3 b. -1 c. - 5 2 d. 1 1 4 e. -5.2 f. 124 Ordering Real Numbers We can express the relationship between two real numbers a and b using symbols of equality and inequality. The equality symbol is the equals sign, =. The inequality symbols are <, >, ≤, ≥, or ≠. The equality and inequality symbols can be used to write mathematical statements. The statement is either true or false. Some examples of true statements are shown. Verbal Statement Mathematical Statement Example Read as a is equal to b a = b 3 = 3 “3 is equal to 3” a is less than b a < b 3 < 4 “3 is less than 4” a is greater than b a > b 3 > 2 “3 is greater than 2” a is less than or a ≤ b 3 ≤ 4 “3 is less than or equal to b equal to 4” a is greater than or equal to b a ≥ b 3 ≥ 2 “3 is greater than or equal to 2” a is not equal to b a ≠ b 1 ≠ 3 “1 is not equal to 3” Objective 3 ▶ Compare the value of two real numbers.


hendricks_beginning_algebra_1e_ch1_3
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