Solving Linear Inequalities in One Variable

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality using inverse operations, similar to solving an equation.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.

Front

Solve the inequality: 10 – 2x ≥ –4

Back

x ≤ 7

Front

What is a compound inequality?

Back

A compound inequality consists of two or more inequalities joined by 'and' or 'or'.

Front

Solve the compound inequality: –10 ≤ 2x + 4 < 22

Back

–7 ≤ x < 9

Front

Solve the inequality: –2x > –10

Back

x < 5

Front

Solve the inequality: –3x + 1 ≤ 13

Back

x ≥ –4

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

How do you graph the solution set of an inequality?

Back

To graph the solution set, draw a number line and use an open circle for < or > and a closed circle for ≤ or ≥, shading the appropriate region.