Inequality

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, greater than or equal to, or less than or equal to the other.

Front

What symbols are used to represent inequalities?

Back

The symbols used are: > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).

Front

What does a closed dot on a number line indicate?

Back

A closed dot indicates that the number is included in the solution set, used for ≤ and ≥ inequalities.

Front

What does an open dot on a number line indicate?

Back

An open dot indicates that the number is not included in the solution set, used for < and > inequalities.

Front

How do you solve the inequality 2x + 1 < -3?

Back

Subtract 1 from both sides: 2x < -4. Then divide by 2: x < -2.

Front

What is the solution to the inequality x ≥ 3?

Back

The solution includes all numbers greater than or equal to 3, represented on a number line with a closed dot at 3.

Front

How do you graph the inequality x + 4 > 2?

Back

First, solve for x: x > -2. Then, graph with an open dot at -2 and shade to the right.

Front

What does the inequality x < -3 represent on a number line?

Back

It represents all numbers less than -3, graphed with an open dot at -3 and shading to the left.

Front

What is the difference between x > 5 and x ≥ 5?

Back

x > 5 means 5 is not included; x ≥ 5 means 5 is included in the solution.

Front

How do you interpret the inequality 3x - 2 ≤ 4?

Back

Add 2 to both sides: 3x ≤ 6. Then divide by 3: x ≤ 2.