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“A student solves the compound inequality 15 is less than or equal to 2x+5 is less than or equal to 17 and finds the solutions of the compound inequality to be all real numbers” can be expressed as:

“15≤2x+5≤17. A student claims that the solution is: x is all real numbers.”

Subtract 5 right across the inequality:

10≤2x≤12.

Now divide throughout by 2:

5≤x≤6.

In words, this means x is between 5 and 6 (inclusive), which can be written as the closed interval [5,6].

So the inequality is only satisfied in this range and excludes x<5 and x>6, so it’s not true under these conditions, and the student’s statement is false.

by Top Rated User (711k points)

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