Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as >, <, ≥, or ≤.

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is any number greater than 5.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 3 means x is any number less than 3.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 4 means x is any number greater than or equal to 4.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 2 means x is any number less than or equal to 2.

Front

How do you solve the inequality 15 > x - 1?

Back

To solve 15 > x - 1, add 1 to both sides: 16 > x, or x < 16.

Front

What is the solution set for the inequality 15 > x - 1?

Back

The solution set is all numbers less than 16, which can include numbers like 1, 7, and 15.

Front

How do you represent a range of values in an inequality?

Back

A range of values can be represented using '≤' and '≥'. For example, 2 ≤ x ≤ 8 means x can be any number from 2 to 8, inclusive.

Front

What is the solution to the inequality 8(m + 2) < 4(5 + 2m)?

Back

The solution is all real numbers, meaning any value of m satisfies the inequality.

Front

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

Back

To graph x < 3, draw an open circle at 3 and shade to the left, indicating all numbers less than 3.