Math Problem Statement

Graph the solution set of the first linear inequality: x > 4 or y ≥ 2.

Solution

In the given problem, you are asked to graph the solution set of the linear inequality x>4x > 4 or y2y \geq 2.

Here is a breakdown of how to proceed with the graphing:

1. Inequality x>4x > 4:

  • This inequality represents a vertical line at x=4x = 4. Since it's a strict inequality, the boundary line will be dashed.
  • We choose two points on the line, such as (4,0)(4, 0) and (4,1)(4, 1), but the line itself will not be part of the solution since x>4x > 4. We will shade the region to the right of the line (where x>4x > 4).

2. Inequality y2y \geq 2:

  • This inequality represents a horizontal line at y=2y = 2. Since it's a non-strict inequality (with \geq), the boundary line will be solid.
  • Choose two points, such as (0,2)(0, 2) and (1,2)(1, 2), and shade the region above the line where y2y \geq 2.

3. Shading the region:

  • Since this is an "OR" inequality, you will shade the regions that satisfy either inequality. This means you will shade the region to the right of x=4x = 4 and the region above y=2y = 2.
  • You can ignore any areas where neither inequality holds.

Input for the Graph:

  • For the boundary line of x=4x = 4:

    • Choose "Dashed" for the line.
    • Points: (4,0)(4, 0), (4,1)(4, 1).
    • Shade to the right (Region B).
  • For the boundary line of y=2y = 2:

    • Choose "Solid" for the line.
    • Points: (0,2)(0, 2), (1,2)(1, 2).
    • Shade above (Region A).

Would you like more details on this process, or any further clarification?


Here are 5 related questions to expand your understanding:

  1. How do you graph inequalities involving both xx and yy?
  2. How would the solution change if the inequality were x4x \geq 4 or y>2y > 2?
  3. What does the union of two inequality regions (OR) represent geometrically?
  4. How do you shade regions for "AND" inequalities, and how is it different from "OR"?
  5. How would you represent inequalities that include variables on both sides, such as 2x+y>42x + y > 4?

Tip: Always check if the inequality includes an "or equal to" condition (like \geq or \leq), as this determines if the boundary line is solid or dashed.

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Math Problem Analysis

Mathematical Concepts

Linear Inequalities
Graphing Inequalities

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12