For this case we must find the solution of the following inequalities:
[tex]-3x + 10 \geq16\ or\ 9-x <7[/tex]
So:
[tex]-3x + 10 \geq16[/tex]
Subtracting 10 from both sides of the inequality:
[tex]-3x \geq16-10\\-3x \geq6[/tex]
Dividing by 3 to both sides of the inequality:
[tex]-x \geq \frac {6} {3}\\-x \geq2[/tex]
We multiply by -1 on both sides taking into account that the sense of inequality changes:
[tex]x \leq-2[/tex]
Thus, the solution is given by all values of x less than or equal to -2.
Also we have:
[tex]9-x <7[/tex]
Subtracting 9 from both sides of the inequality:
[tex]-x <7-9\\-x <-2[/tex]
We multiply by -1 on both sides taking into account that the sense of inequality changes:
[tex]x> 2[/tex]
Thus, the solution is given by all values of x greater than 2.
Therefore, the solution set is given by:
(-∞, -2] U (2, ∞)
Answer:
(-∞, -2] U (2, ∞)
