Question

-15x + 4 < 109 or -6x + 70 > - 2

Answer 1

For this case we must find the solution set of the given inequalities:

$-15x + 4 <109$

We subtract 4 from both sides of the inequality:

$-15x <109-4\\-15x <105$

We divide between 15 on both sides of the inequality:

$-x <\frac {105} {15}\\-x <7$

We multiply by -1 on both sides taking into account that the sense of inequality changes:

$x> -7$

The solution is given by all values of x greater than -7.

$-6x + 70> -2$

Subtracting 70 from both sides of the inequality:

$-6x> -2-70\\-6x> -72$

We divide by 6 on both sides of the inequality:

$-x> - \frac {72} {6}\\-x> -12$

We multiply by -1 on both sides taking into account that the sense of inequality changes:

$x <12$

Thus, the solution set is given by:

$x> -7\ U\ x <12$

Therefore the solution is all real numbers.

Answer:

All real numbers.