For this case we must find the solution set of the given inequalities:
Inequality 1:
[tex]3 (2x + 1)> 21[/tex]
Applying distributive property on the left side of inequality:
[tex]6x + 3> 21[/tex]
Subtracting 3 from both sides of the inequality:
[tex]6x> 21-3\\6x> 18[/tex]
Dividing by 6 on both sides of the inequality:
[tex]x> \frac {18} {6}\\x> 3[/tex]
Thus, the solution is given by all the values of "x" greater than 3.
Inequality 2:
[tex]4x + 3 <3x + 7[/tex]
Subtracting 3x from both sides of the inequality:
[tex]4x-3x + 3 <7\\x + 3 <7[/tex]
Subtracting 3 from both sides of the inequality:
[tex]x <7-3\\x <4[/tex]
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
