For this case we must find the solution of the following system of inequalities:
[tex]3x-4 \leq2[/tex] or [tex]2x + 11 \geq-1[/tex]
Inequality 1:
[tex]3x-4 \leq2[/tex]
We add 4 to both sides of the inequality:
[tex]3x \leq2 + 4\\3x \leq6[/tex]
We divide between 3 on both sides of the inequality:
[tex]x \leq \frac {6} {3}\\x \leq2[/tex]
Thus, the solution is given by all values of x less than or equal to 2.
Inequality 2:
[tex]2x + 11 \geq-1[/tex]
We subtract 11 from both sides of the inequality:
[tex]2x \geq-1-11\\2x \geq-12[/tex]
We divide between 2 on both sides of the inequality:
[tex]x \geq \frac {-12} {2}\\x \geq-6[/tex]
Thus, the solution is given by all values of x greater than or equal to -6.
Thus, the solution set is given by:
(-∞, - 2] U [-6,∞)
That is, the solution set is given by all real numbers.
Answer:
All real numbers
