Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or equal to the other.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 5 means x is any number less than 5.

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is any number greater than 3.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x can be any number less than or equal to 4.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x can be any number greater than or equal to 2.

Front

How do you solve the inequality x + 5 < 10?

Back

Subtract 5 from both sides: x < 5.

Front

How do you solve the inequality 2x - 3 ≥ 7?

Back

Add 3 to both sides: 2x ≥ 10, then divide by 2: x ≥ 5.

Front

What is the solution to the inequality 4k + 15 > -2k + 3?

Back

Combine like terms: 6k > -12, then divide by 6: k > -2.

Front

How do you graph the inequality x < 3 on a number line?

Back

Draw an open circle at 3 and shade to the left to indicate all numbers less than 3.

Front

What is the solution to the inequality 10 ≥ x - 3?

Back

Add 3 to both sides: 13 ≥ x, or x ≤ 13.