Options
[tex](A)\left(-\infty , \dfrac23\right]\\\\(B)\left(-\infty , \dfrac23\right) \\\\(C)(\frac23\right, \infty ) \\\\(D) [\frac23\right, \infty )[/tex]
Answer:
[tex](C)(\frac23\right, \infty )[/tex]
Step-by-step explanation:
Given the solution to an inequality
{x|x>2/3}
The solution set does not include [tex]\dfrac23[/tex] , 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 [tex]\dfrac23[/tex] , the solution set contains all values of larger than [tex]\dfrac23[/tex] 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:
[tex](\frac23\right, \infty )[/tex]
The correct option is C.
