Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (>, <, ≥, ≤) to show that one expression is greater than, less than, or equal to another.

Front

What does the symbol '≤' represent?

Back

The symbol '≤' means 'less than or equal to'. It indicates that a value can be either less than or exactly equal to another value.

Front

What does the symbol '≥' represent?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that a value can be either greater than or exactly equal to another value.

Front

How do you represent the solution to the inequality x > 5 on a number line?

Back

You use an open circle at 5 and shade to the right, indicating that 5 is not included in the solution.

Front

How do you represent the solution to the inequality x ≤ 3 on a number line?

Back

You use a closed circle at 3 and shade to the left, indicating that 3 is included in the solution.

Front

What is the solution to the inequality 2x + 3 < 11?

Back

x < 4.

Front

What is the solution to the inequality -3x + 5 ≥ 2?

Back

x ≤ 1.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

Front

What is the difference between an open circle and a closed circle on a graph?

Back

An open circle indicates that the number is not included in the solution (for > or <), while a closed circle indicates that the number is included (for ≥ or ≤).

Front

How do you solve the inequality 4 - 2x > 10?

Back

x < -3.