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 not equal to the other.

Front

What does the symbol '<' represent 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 '>' represent 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 '≤' represent 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 '≥' represent 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 -2(x + 2) < 14?

Back

First, distribute -2: -2x - 4 < 14. Then, add 4 to both sides: -2x < 18. Finally, divide by -2 (remember to flip the inequality): x > -9.

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Back

Front

How do you write an inequality for 'Twenty-two more than four times a number is less than 82'?

Back

The inequality is written as: 22 + 4n < 82.

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Back

The solution is all values of x that are less than -1.1.

Front

What is the first step in solving the inequality 4n + 22 < 82?

Back

Subtract 22 from both sides: 4n < 60.