Solutions to Inequalities

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 does the symbol '≥' represent in inequalities?

Back

'≥' means 'greater than or equal to'.

Front

What does the symbol '≤' represent in inequalities?

Back

'≤' means 'less than or equal to'.

Front

How do you solve the inequality 10 ≥ x - 3?

Back

To solve, add 3 to both sides: 10 + 3 ≥ x, which simplifies to 13 ≥ x or x ≤ 13.

Front

What is the solution set for the inequality x + 5 ≤ 13?

Back

The solution set is x ≤ 8.

Front

How do you express 'the distance, d, is at least 110 miles' as an inequality?

Back

The inequality is d ≥ 110.

Front

Is x = 2 a solution to the inequality x + 2 > 3?

Back

Yes, because substituting x = 2 gives 2 + 2 > 3, which is true.

Front

How do you read the inequality z < 10?

Back

You read it as 'z is less than 10'.

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.

Front

How do you graph the inequality x < 5 on a number line?

Back

Draw an open circle at 5 and shade to the left to indicate all numbers less than 5.