What is the solution to the inequality shown in the diagram?
We have hundreds of course questions with personalized recommendations + Account 100% premium
What is the solution to the inequality shown in the diagram?
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 is . The filled circle means 3 itself is part of the solution.
Thus, the solution to the inequality represented by the diagram is:
This matches with choice number 3 in the provided options: .
Solve the following inequality:
\( 3x+4 \leq 10 \)
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).
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 .
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.
Pick any number from your solution and see if it makes sense! Try x = 5: Is ? Yes! Try x = 0: Is ? No, so 0 shouldn't be in the shaded region.
Both and 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.'
Get unlimited access to all 18 Inequality questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime