1.6 Inequalities

Front

What is an inequality?

Back

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

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. For example, 6 > x means 6 is greater than x.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. For example, k < 3 means k is less than 3.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 10 means x is less than or equal to 10.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ -10 means x is greater than or equal to -10.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

First, subtract 14 from both sides: -4x ≤ 40. Then, divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What happens to the inequality symbol when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol.

Front

How do you graph the inequality k < 3?

Back

To graph k < 3, draw a number line, place an open circle at 3, and shade to the left to indicate all values less than 3.

Front

What is the solution to the inequality 4x - 3 < -1x + 12?

Back

To solve, combine like terms: 5x < 15. Then divide by 5: x < 3.

Front

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

Back

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