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>2/3. What is another way to represent the solution set?

Answer 1

Options

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

Answer:

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

Explanation:

Given the solution to an inequality

x

The solution set does not include
`\frac23` , 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
`\frac23` , the solution set contains all values of larger than
`\frac23` 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 is:

`(\frac23\right, \infty )`

The correct option is C.