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?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you solve the inequality 4x + 5 ≥ 41?

Back

Subtract 5 from both sides: 4x ≥ 36. Then divide by 4: x ≥ 9.

Front

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

Back

The inequality sign flips when you multiply or divide both sides by a negative number.

Front

Solve the inequality 10 < 3x + 19.

Back

Subtract 19 from both sides: -9 < 3x. Then divide by 3: -3 < x or x > -3.

Front

What is the solution to the inequality -7x + 15 ≥ -20?

Back

Subtract 15 from both sides: -7x ≥ -35. Then divide by -7 (flipping the sign): x ≤ 5.

Front

What does the number line represent in inequalities?

Back

A number line visually represents the solutions to an inequality, showing which values satisfy the inequality.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to.

Front

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

Back

Draw a solid dot on 3 and shade to the right to indicate all numbers greater than or equal to 3.