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

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

Front

What does the symbol '<' mean in inequalities?

Back

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

Front

What does the symbol '≥' mean in inequalities?

Back

'≥' 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

'≤' 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 2x + 3 < 11?

Back

Subtract 3 from both sides: 2x < 8. Then divide by 2: x < 4.

Front

What is the solution to the inequality 3x - 5 ≥ 1?

Back

Add 5 to both sides: 3x ≥ 6. Then divide by 3: x ≥ 2.

Front

How do you graph the inequality x < 4 on a number line?

Back

Draw an open circle at 4 and shade to the left to indicate all numbers less than 4.

Front

What is the solution to the inequality 4x - 2 ≤ -22?

Back

Add 2 to both sides: 4x ≤ -20. Then divide by 4: x ≤ -5.

Front

What does the solution x > -28 represent on a number line?

Back

It represents all numbers greater than -28, shown with an open circle at -28 and shading to the right.