“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:
Now divide throughout by 2:
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.