Question

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

Answer 1

For this case we must find the solution set of the given inequalities:

Inequality 1:

$3 (2x + 1)> 21$

Applying distributive property on the left side of inequality:

$6x + 3> 21$

Subtracting 3 from both sides of the inequality:

$6x> 21-3\\6x> 18$

Dividing by 6 on both sides of the inequality:

$x> \frac {18} {6}\\x> 3$

Thus, the solution is given by all the values of "x" greater than 3.

Inequality 2:

$4x + 3$

Subtracting 3x from both sides of the inequality:

$4x-3x + 3$

Subtracting 3 from both sides of the inequality:

$x$

Thus, the solution is given by all values of x less than 4.

The solution set is given by the union of the two solutions, that is, all real numbers.

Answer:

All real numbers