Solving Linear Inequalities

Front

Define a linear inequality.

Back

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

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 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 does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or equal to the number.

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the number.

Front

Solve the inequality: 2x + 5 < 15.

Back

x < 5.

Front

Solve the compound inequality: 4 ≤ 2x - 3 < 10.

Back

3.5 ≤ x < 6.5.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities into one statement, often using 'and' or 'or'.

Front

Solve the compound inequality: -2 < 3x + 1 ≤ 7.

Back

-1 < x ≤ 2.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the endpoints, while non-strict inequalities (≤, ≥) do include the endpoints.