Answer:
Given the system of inequalities: [tex]37-3x>4x-2[/tex]
Add 2 to both sides of the equation, we have;
[tex]39-3x > 4x[/tex]
Add 3 to both sides we have;
[tex]39>7x[/tex]
Divide both sides by 7 we get;
[tex]x < \frac{39}{7}[/tex]
The solution set for this inequality is: [tex](-\infty, \frac{39}{7})[/tex]
Given the system of inequalities: [tex]19x-51\geq 5x+27[/tex]
Add 51 to both sides of the equation, we have;
[tex]19 \geq 5x+78[/tex]
Subtract 5x from both sides we have;
[tex]14x \geq 78[/tex]
Divide both sides by 14 we get;
[tex]x \geq \frac{78}{14} = \frac{39}{7}[/tex]
or
[tex]x \geq \frac{39}{7}[/tex]
The solution set for this inequality is: [tex][\frac{39}{7}, \infty)[/tex]
The combined solution for this system of inequality is; [tex](-\infty, \frac{39}{7}) \cap[\frac{39}{7}, \infty)[/tex] = ∅
