Inequalities

Front

What does the symbol '≥' represent in inequalities?

Back

It represents 'greater than or equal to'.

Front

What does the symbol '≤' represent in inequalities?

Back

It represents 'less than or equal to'.

Front

How do you solve the inequality -3(x + 2) < 21?

Back

First, distribute -3: -3x - 6 < 21. Then, add 6 to both sides: -3x < 27. Finally, divide by -3 (remember to flip the inequality): x > -9.

Front

How do you solve the inequality 3x - 10 > 2?

Back

First, add 10 to both sides: 3x > 12. Then, divide by 3: x > 4.

Front

What inequality corresponds to the graph that shows all values less than 3?

Back

The inequality is x < 3.

Front

What is the solution set for the inequality x ≥ 5?

Back

The solution set includes all real numbers greater than or equal to 5.

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 include the boundary point.

Front

How do you graph the inequality x < 2 on a number line?

Back

Draw an open circle at 2 and shade to the left to indicate all numbers less than 2.

Front

What is the solution to the compound inequality 1 < x ≤ 4?

Back

The solution includes all numbers greater than 1 and less than or equal to 4.

Front

How do you solve the inequality 2x + 3 > 7?

Back

Subtract 3 from both sides: 2x > 4. Then, divide by 2: x > 2.