Which graph represents the solutions to the inequality |2x − 6| less than or equal to 10?
Inequalities are one of the most important concepts in mathematics. Let's solve a problem related to this concept.
Answer: The graph which represents the inequality |2x − 6| less than or equal to 10 has bounded x-coordinates from x = -2 to x = 8, but has unbounded y-coordinates.
Let's understand the solution step by step.
To represent |2x − 6| ≤ 10 in the graph, we have to consider two cases:
- Case 1: In this case, the inequality becomes -(2x - 6) ≤ 10 → -2x + 6 ≤ 10. Finally, this inequality becomes x ≥ -2.
- Case 2: In this case, the inequality becomes (2x - 6) ≤ 10. Finally, it becomes x ≤ 8.
Hence, the range covered by x is [-2, 8].
The graph of the given inequality is unbounded in y-axis.
The figure below represents the graph of the inequality.