Linear Inequalities — Chapter Summary

Two real numbers or two algebraic

Two real numbers or two algebraic expressions related by <, >, ≤, or ≥ form an inequality. An inequality becomes true only for certain values of the v

Strict inequalities use < or >

Strict inequalities use < or >. Slack inequalities use ≤ or ≥. For example, ax + b < 0 is strict, while ax + b ≤ 0 is slack.

Expressions of the form ax +

Expressions of the form ax + b < 0, ax + b > 0, ax + b ≤ 0, or ax + b ≥ 0 with a ≠ 0 are linear inequalities in one variable.

Expressions of the form ax +

Expressions of the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c with a ≠ 0 and b ≠ 0 are linear inequalities in two variables.

Equal numbers may be added

Equal numbers may be added to or subtracted from both sides of an inequality without affecting the sign of inequality.