Question

Solve for X, and graph
8. - 6x + 14 <-28 OR 9x + 15 <- 12

Answer 1

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

$-6x + 14 <-28$

Subtracting 14 from both sides of the inequality we have:

$-6x <-28-14\\-6x <-42$

Dividing by 6 on both sides of the inequality:

$-x <- \frac {42} {6}\\-x <-7$

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

$x> 7$

Thus, the solution is given by all values of x greater than 7.

On the other hand we have:

$9x + 15 <-12$

Subtracting 15 from both sides of the inequality we have:

$9x <-12-15\\9x <-27$

Dividing between 9 on both sides of the inequality we have:

$x <- \frac {27} {9}\\x <-3$

Thus, the solution is given by all values of x less than -3.

Finally, the solution set is:

(-∞, - 3) U (7,∞)

Answer:

(-∞, - 3) U (7,∞)