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

'≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'.

Front

How do you solve the inequality x + 5 ≤ 13?

Back

Subtract 5 from both sides: x ≤ 8.

Front

What is the solution to the inequality 4h < 8?

Back

Divide both sides by 4: h < 2.

Front

How do you isolate the variable in the inequality -4 - 6m > -9m + 8?

Back

Add 9m to both sides and then add 4 to both sides: 3m > 12, so m > 4.

Front

What does it mean if an inequality has no solutions?

Back

It means there are no values for the variable that can satisfy the inequality.

Front

What is the solution to the inequality -5(w - 4) < -5w - 15?

Back

No solutions to this inequality.

Front

How do you graph the inequality x < 5?

Back

Draw a number line, place an open circle at 5, and shade to the left.

Front

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

Back

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