For this case we must find the solution set of the given inequalities:
[tex]-15x + 4 <109[/tex]
We subtract 4 from both sides of the inequality:
[tex]-15x <109-4\\-15x <105[/tex]
We divide between 15 on both sides of the inequality:
[tex]-x <\frac {105} {15}\\-x <7[/tex]
We multiply by -1 on both sides taking into account that the sense of inequality changes:
[tex]x> -7[/tex]
The solution is given by all values of x greater than -7.
[tex]-6x + 70> -2[/tex]
Subtracting 70 from both sides of the inequality:
[tex]-6x> -2-70\\-6x> -72[/tex]
We divide by 6 on both sides of the inequality:
[tex]-x> - \frac {72} {6}\\-x> -12[/tex]
We multiply by -1 on both sides taking into account that the sense of inequality changes:
[tex]x <12[/tex]
Thus, the solution set is given by:
[tex]x> -7\ U\ x <12[/tex]
Therefore the solution is all real numbers.
Answer:
All real numbers.
