Math Problem Statement

Select the compound inequality shown on the graph.

Solution

The graph shows a number line with a compound inequality, indicated by the orange shading between 1-1 and 66, where 1-1 has an open circle and 66 has a closed circle.

This implies:

  • The inequality is strict at 1-1 (open circle), meaning x>1x > -1.
  • The inequality is inclusive at 66 (closed circle), meaning x6x \leq 6.

Thus, the correct inequality is: 1<x6-1 < x \leq 6 Which corresponds to option B.

Would you like a more detailed explanation or have any questions?

Here are five related questions you might explore:

  1. How would the inequality change if both endpoints were open circles?
  2. What if the endpoint at 66 were also an open circle?
  3. Can you graph the inequality 2x<4-2 \leq x < 4?
  4. How do you represent inequalities on a number line using set notation?
  5. How do you solve compound inequalities algebraically?

Tip: When reading inequalities from a graph, always pay attention to whether the circles are open or closed to determine strictness or inclusiveness.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Number Line
Compound Inequality

Formulas

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Theorems

Basic properties of inequalities on number lines

Suitable Grade Level

Grades 6-8