Question - Graphing an Inequality on a Number Line
Solution:
The inequality given in the image is $$ t \geq -3 $$. To graph this inequality on a number line:1. Locate the point -3 on the number line.2. Since the inequality includes "greater than or equal to" (as indicated by the symbol $$\geq$$), you need a solid circle or dot at -3. This shows that -3 is part of the solution set.3. Shade the number line to the right of -3, indicating all numbers greater than -3 are also included in the solution set.Now let's examine the provided options to see which graph corresponds to these instructions:A. This graph shows a number line with a solid dot at -3 and shading towards the left, which means values less than -3. This does not match the inequality.B. This graph shows a number line with an open circle at -3 (indicating that -3 is not included) and shading towards the right. This is not correct because the inequality specifies that -3 is included.C. This graph shows a number line with a solid dot at -3 and shading to the right, which seems to match the inequality $$ t \geq -3 $$.D. This graph depicts a number line with a solid dot at 3 and shading to the right; however, this does not correspond to the inequality provided.The correct answer is C, as it correctly represents the inequality $$ t \geq -3 $$.
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