Question

The solution to an inequality is represented by the number line. A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5. How can this same solution be written using set-builder notation?

1) x | x > 3
2) x | x < 3
3) x | x ≥ 3
4) x | x ≤ 3

Answer 1

The number line showing an open circle at positive 3 and shading to positive 5 denotes an inequality which is represented in set-builder notation as x > 3, which is option 1.

Step-by-step explanation:

The solution to the inequality represented on a number line with an open circle at positive 3 and shaded from positive 3 to positive 5 can be written using set-builder notation. The open circle at positive 3 indicates that 3 is not included in the solution set, and the shading from 3 to 5 shows that every number greater than 3 and up to 5 is part of the solution set. In set-builder notation, this is written as x > 3, which corresponds to option 1.