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Graphing real numbers on the number line (A) To graph the real numbers that are greater than or equal to 3 on a number line, we would need to plot a point starting at 3 and on every single number to its right. This is practically an impossible task. Instead, we only need to draw a solid dot on the 3 and draw a thick or bold line to the right of 3, all the way to infinity (which we specify with an arrow head). So, if we let x represent any real number, the corresponding graph for x ≥ 3 is: -5 -4 -3 -2 -1 0 1 2 3 4 5 Suppose we now want all the numbers that are greater than 3, that is, not including the 3. Then we use an open circle. The graph for x > 3 would be: -5 -4 -3 -2 -1 0 1 2 3 4 5 Note: Remember that the symbol ≥ is used for greater than or equal to, and the symbol > represents greater than (that is, not including the given number). (B) Let us now graph the real numbers that are less than or equal to 3 on a number line. Since x ≤ 3,we want to include the 3 and we use a solid dot, like this: -4 -3 -2 -1 0 1 2 3 4 5 The graph for x < 3 is shown next. Observe that we want the real numbers less that 3, but not including the 3, thus the open circle. -4 -3 -2 -1 0 1 2 3 4 5 Note: Remember that the symbol ≤ is used for less than or equal to, and the symbol < represents less than (that is, not including the given number). Example 1 Write the inequality that corresponds to the given graph. -5 -4 -3 -2 -1 0 1 2 3 4 5 Answer: x ≥ -5 Example 2 Choose the inequality that matches the given graph. Page 1 of 3 -5 -4 -3 -2 -1 a. x > -2 0 1 2 3 4 b. x < -2 5 c. x > -1.5 d. x < -1.5 Answer: c Example 3 Choose the graph that corresponds to the inequality x ≤ -2 a. -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 b. c. d. -5 -4 -3 -2 -1 0 1 2 3 4 5 Answer: a Your turn to practice these problems! (See Answer key on next page) 1. Use a number line to graph each of the following: a. x ≤ -1 b. x ≥ -4 c. x < 4 d. x >0 e. x ≤ 0 2. Write the inequality that corresponds to the given graph. a. b. -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Page 2 of 3 Answer Key for Practice Problems 1. a -4 -3 -2 -1 0 1 2 3 4 5 3 4 5 3 4 5 3 4 5 3 4 5 b. -5 -4 -3 -2 -1 0 1 2 c. -4 -3 -2 -1 0 1 2 d. -5 -4 -3 -2 -1 0 1 2 e. -4 -3 -2 -1 0 1 2 2. a. x > -3.5 b. x ≤ 5 Page 3 of 3