Chapter 1 sections 4-6

A compound inequality is an inequality that combines two or more inequalities using the words 'and' or 'or'. For example, $$x < 5 \text{ and } x > 1$$ .

To solve a compound inequality with 'and', find the intersection of the solution sets of the individual inequalities.

To solve a compound inequality with 'or', find the union of the solution sets of the individual inequalities.

First, simplify: $$3x + 9 - 2 < 4$$ , which leads to $$3x < -3$$ , so $$x < -1$$ .

First, simplify: $$2x - 3 + x > x + 1$$ , which leads to $$2x - 3 > 1$$ , so $$x > 2$$ .

The formula represents the actual cost, $$a$$ , of an item with original price $$m$$ after a coupon for $$n$$ dollars off is applied.

Rearranging gives $$n = m - a$$ .

The solution is $$x < 14 \text{ and } x \text{ ≥ } \frac{2}{3}$$ .

The solution is $$3 < x < 7$$ .

The first step is to isolate the variable in the inequalities.