Question

The solution to an any quality is giving in the same building notation as The solution to an inequality is giving in the set builder notation as {x|x>2/3}. What is another way to represent the solution set?

Answer 1

Options

$(A)\left(-\infty , \dfrac23\right]\\\\(B)\left(-\infty , \dfrac23\right) \\\\(C)(\frac23\right, \infty ) \\\\(D) [\frac23\right, \infty )$

Answer:

$(C)(\frac23\right, \infty )$

Step-by-step explanation:

Given the solution to an inequality

{x|x>2/3}

The solution set does not include $\dfrac23$ , therefore, it must be open at the left. Recall that we use a curvy bracket ( to denote openness at the left.

Since x is greater than  $\dfrac23$ , the solution set contains all values of larger than  $\dfrac23$ up till infinity. Since infinity is an arbitrarily large value, we also use an open bracket at the right.

Therefore, another way to represent the solution {x|x>2/3} is:

$(\frac23\right, \infty )$

The correct option is C.