Analyze the Number Line: Solving the Diagram's Inequality from -4 to 3

Number Line Inequalities with Filled Circles

What is the solution to the inequality shown in the diagram?

-43

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1

Understand the problem

What is the solution to the inequality shown in the diagram?

-43

2

Step-by-step solution

The task is to interpret the inequality shown by a number line diagram.

First, observe the number line diagram provided. The numbers -4 and 3 are highlighted with vertical dashed lines. A critical point is at 3, where the circle is filled, indicating the inclusion of this point in the set. The line then extends from 3 to the right, suggesting that any point greater than or equal to 3 is included.

This indicates the inequality for x x is x3 x \geq 3 . The filled circle means 3 itself is part of the solution.

Thus, the solution to the inequality represented by the diagram is:

3x 3 \leq x

This matches with choice number 3 in the provided options: 3x 3 ≤ x .

3

Final Answer

3x 3 ≤ x

Key Points to Remember

Essential concepts to master this topic
  • Circle Type: Filled circle means the endpoint is included (≤ or ≥)
  • Direction: Arrow or shading shows which values are part of solution
  • Check: Test a point in the shaded region: x = 4 satisfies 3 ≤ x ✓

Common Mistakes

Avoid these frequent errors
  • Confusing filled and open circles
    Don't think a filled circle means 'not included' = wrong inequality symbol! A filled circle shows the endpoint IS part of the solution. Always remember: filled circle = ≤ or ≥, open circle = < or >.

Practice Quiz

Test your knowledge with interactive questions

Solve the following inequality:

\( 3x+4 \leq 10 \)

FAQ

Everything you need to know about this question

How do I tell if a circle is filled or open?

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A filled (solid) circle looks completely colored in, while an open circle is just an outline. Think of it like a target - filled means 'hit' (included), open means 'missed' (not included).

What does the arrow pointing right mean?

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The arrow shows that all numbers greater than 3 are part of the solution. Since the circle at 3 is filled, we include 3 too, giving us x3 x ≥ 3 .

Why isn't -4 part of the solution?

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The number -4 just marks a reference point on the number line. The actual solution starts at 3 (filled circle) and goes right. The -4 has no circle at all, so it's not included.

How can I double-check my answer?

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Pick any number from your solution and see if it makes sense! Try x = 5: Is 53 5 ≥ 3 ? Yes! Try x = 0: Is 03 0 ≥ 3 ? No, so 0 shouldn't be in the shaded region.

What if I wrote 3 ≤ x instead of x ≥ 3?

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Both 3x 3 ≤ x and x3 x ≥ 3 mean exactly the same thing! It's like saying 'three is less than or equal to x' versus 'x is greater than or equal to three.'

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