2.5-2.6 pratice 2024

The inequality $$|x| \ge 5$$ means that x is either greater than or equal to 5 or less than or equal to -5. In interval notation, this is expressed as $$(-\infty, -5] \cup [5, \infty)$$ .

To solve $$|x + 1| < 6$$ , you split it into two inequalities: -6 < x + 1 < 6. Solving these gives -7 < x < 5.

A compound inequality combines two inequalities, often using 'and' or 'or'. For example, $$-2 < x \le 2$$ is a compound inequality.

To graph $$-5 \le x < 0$$ , draw a solid dot at -5 (included) and an open dot at 0 (not included), shading the region between them.

This inequality means that x can be any value greater than 2 or any value less than or equal to -3.

The solution set for $$|x| < 4$$ is -4 < x < 4, which means x is between -4 and 4, not including -4 and 4.

The inequality $$x \ge 3$$ means that x can be 3 or any number greater than 3.

In compound inequalities, 'and' means both conditions must be true simultaneously, while 'or' means at least one condition must be true.

To solve $$|x - 2| \le 5$$ , split it into two inequalities: -5 \le x - 2 \le 5. This gives the solution set -3 \le x \le 7.

The notation $$(-\infty, a)$$ represents all real numbers less than a.