Question

Which of the following sets would have a graph with an open circle on 5 and a ray pointing left on the number line?


{x | xR, x ≤ 5}
{x | xR, x > 5}
{x | xR, x < 5}

Answer 1

For an inequality, an open circle on the number line means that the number is NOT included in the set. The arrow points in the direction that you look to find all possible values for x. In the case you've given us, the open circle on 5 means that 5 is not included in the set, and the arrow pointing to the right (i.e. to the greater values) means that x will be equal to the set of all positive real numbers greater than but not including 5. So

{x|x > 5, x ∈ ℝ}


In answer A, since 5 is included in the set, it would be indicated with a solid (or closed) dot at 5. And in both A and C, the arrow would point to the left, showing that x is the set of all values less than, or less than or equal to, 5