Math Problem Statement
Can you guide me how to graph this
Can you guide me how to graph this inequality: x < -6?
Solution
To graph the inequality on the coordinate plane, follow these steps:
-
Draw the boundary line:
- The inequality involves , which means it's a vertical line.
- The equation of the boundary line is . Draw a vertical dotted line through to indicate that points on this line are not included in the solution (since the inequality is strictly "<").
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Shade the appropriate region:
- Since the inequality is , you need to shade the region to the left of the line . This represents all the points where is less than -6.
The dotted line indicates that the boundary itself is not included in the solution (as the inequality does not include but only values less than it).
Would you like more details or have any questions?
Related questions:
- How would the graph change if the inequality was ?
- What does the inequality look like graphically?
- How can we graph a system of inequalities involving and another inequality?
- How does the graph of compare to ?
- What is the meaning of shading in inequalities like this one?
Tip: Use a solid line when the inequality includes "equal to" (like or ). A dotted line is used for strict inequalities (like or ).
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Inequalities
Graphing Inequalities
Formulas
x = c for vertical lines
Theorems
Graphing inequalities
Boundary lines and shading in inequalities
Suitable Grade Level
Grades 7-10