Which is the best interpretation of the solution set for the compound inequality?3(2x + 1) > 21 or 4x + 3 < 3x +7no solution3Ox<3 or x > 4all real numbers

Accepted Solution

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