Математика15 мин

Linear Inequalities

Solve linear inequalities and compound systems, and remember the rule about flipping the sign.

Solving rules

Treat an inequality like an equation, with one twist: when you multiply or divide both sides by a **negative number**, flip the inequality sign.

Flip the sign

Solve $-2x + 5 > 11$ .

Жауап: $x < -3$

The most common mistake is forgetting to flip when dividing by a negative.

|x| < a \iff -a < x < a

|x| > a \iff x < -a \text{ or } x > a

Compound

Solve $-3 < 2x + 1 \le 7$ .

Жауап: $x \in (-2, 3]$

Жаттығу

Solve $|x - 2| \le 5$ .

Жауап пен түсініктемені көру

Жауап: $-3 \le x \le 7$

$-5 \le x - 2 \le 5 \Rightarrow -3 \le x \le 7$ .