Question

Which is the best interpretation of the solution set for the compound inequality?

3(2x + 1) > 21 or 4x + 3 < 3x + 7

Answer 1

(-∞, ∞)

Explanation:

Let's solve each inequality separately.

`\begin{array}{rcl}3(2x + 1) & > & 21\\2x+1 & > & 7\\2x & > & 6\\x & > & 3\\\end{array}`

`\begin{array}{rcl}4x + 3& < & 3x + 7\\x + 3 & < & 7\\x & < & 4\\\end{array}`

The solution is x > 3 or x < 4

Since x could be less than 4 or greater than 3, x could be any number.

The best interpretation for the solution set is (-∞, ∞).