Inequalities in One Variable

Question 82780 • Online Algebra, Function, Number A

The solution to an inequality is (–∞, 6.5]. Is 6.5 a solution to the inequality? Explain your answer.

Answer

The solution includes numbers from negative infinity to 6.5. Because a bracket is used, the solution does not include 6.5.

The solution includes numbers from 6.5 to infinity. Because a parenthesis is used, the solution does not include 6.5.

The solution is the point (–∞, 6.5). Because a bracket is used, 6.5 is a solution to the inequality.

The solution includes numbers from negative infinity to 6.5. Because a bracket is used, the solution includes 6.5.

Explanation

The interval (–∞, 6.5] includes every number less than or equal to 6.5. The square bracket at 6.5 means that endpoint is included, so 6.5 is a solution. Choice D correctly explains this.

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