Compound InequalitiesBy Miles Tran and Darren Fan

Vocabulary• Inequality- A mathematical sentence built from expressions

using one or more of the symbols <, >, ≤, or ≥

• Graph- The picture obtained by plotting all the points of an equation or inequality

• Coordinate Plane- The plane formed by a horizontal axis and a vertical axis, often labeled the x-axis and the y-axis respectively

• Solution- Any and all value(s) of the variable(s) that satisfies an equation, inequality, system of equations, or system of inequalities

Vocabulary Cont.• Compound Inequalities- Two or more inequalities

taken together. Often this refers to a connected chain of inequalities

• “AND” Inequality- Two inequalities (compound inequalities) combined with the term “AND”

• “OR” Inequality- Two inequalities (compound inequalities) combined with the term “OR”

Prior Knowledge• How to solve inequalities• How to graph inequalities• How to simplify inequalities• How to graph• How to use a number line• How to verify your work

Basics of Compound Inequalities• There are two types of compound inequalities

“AND” and “OR” inequalities• When compound inequalities only contain one

variable, it is graphed on a number line• When compound inequalities contain more than

one variable, they are graphed on a coordinate plain

• To solve a compound inequality separate it into two separate inequalities

• Remember that you must simplify an inequality before you can solve it, this is the same for compound inequalities.

“AND” Inequalities• “AND” Inequalities are 1 of the 2 types of

compound Inequalities• When solving “AND” Inequalities, both inequalities

must be true for the compound inequality to be true

• When graphed, an “AND” inequality forms two points on the same line pointing in opposite directions.

“OR” Inequalities• The “OR” inequality is the other of the two types

of compound inequalities• When you have an “OR” inequality, only one of

the two inequalities has to be true for the compound inequality to be true

• “OR” inequalities form a line segment when graphed

Examples Of Compound Inequalities• Ex: x > -1 and x < 2

• Ex: x < -1 or x > 2