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 x<6x < -6 on the coordinate plane, follow these steps:

  1. Draw the boundary line:

    • The inequality involves xx, which means it's a vertical line.
    • The equation of the boundary line is x=6x = -6. Draw a vertical dotted line through x=6x = -6 to indicate that points on this line are not included in the solution (since the inequality is strictly "<").
  2. Shade the appropriate region:

    • Since the inequality is x<6x < -6, you need to shade the region to the left of the line x=6x = -6. This represents all the points where xx is less than -6.

The dotted line indicates that the boundary itself is not included in the solution (as the inequality does not include x=6x = -6 but only values less than it).

Would you like more details or have any questions?

Related questions:

  1. How would the graph change if the inequality was x6x \leq -6?
  2. What does the inequality x>6x > -6 look like graphically?
  3. How can we graph a system of inequalities involving x<6x < -6 and another inequality?
  4. How does the graph of x<6x < -6 compare to y<6y < -6?
  5. What is the meaning of shading in inequalities like this one?

Tip: Use a solid line when the inequality includes "equal to" (like \leq or \geq). 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