Solve each inequality separately:
1. [tex]2x+3<19.[/tex]
Subtract 3 from both sides of the inequality
[tex]2x+3-3<19-3,\\ \\2x<16.[/tex]
Divide the inequality by 2
[tex]x<8.[/tex]
2. [tex]2x-3\le -7.[/tex]
Add 3 to both sides of the inequality
[tex]2x-3+3\le -7+3,\\ \\2x\le -4.[/tex]
Divide the inequality by 2
[tex]x\le -2.[/tex]
3. The solution set for the system of two inequalities is
[tex]x\le -2[/tex]
or in other words [tex](-\infty,-2].[/tex]
Answer: [tex](-\infty,-2].[/tex]
