2 Answers

Xlogic · Answer 1 · 2020-04-16T15:48:25+0000

For this case we must find the solution of the following system of inequalities:

$3x-4 \leq2$ or
$2x + 11 \geq-1$

Inequality 1:

$3x-4 \leq2$

We add 4 to both sides of the inequality:

$3x \leq2 + 4\\3x \leq6$

We divide between 3 on both sides of the inequality:

$x \leq \frac {6} {3}\\x \leq2$

Thus, the solution is given by all values of x less than or equal to 2.

Inequality 2:

$2x + 11 \geq-1$

We subtract 11 from both sides of the inequality:

$2x \geq-1-11\\2x \geq-12$

We divide between 2 on both sides of the inequality:

$x \geq \frac {-12} {2}\\x \geq-6$

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

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