Solving Inequalities

Front

What does the inequality x > 2 represent on a number line?

Back

It represents all numbers greater than 2, shown with an open circle at 2 and a line extending to the right.

Front

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

Back

Subtract 3 from both sides to get 2x < 4, then divide by 2 to find x < 2.

Front

When graphing the inequality x < 5, what type of circle is used?

Back

An open circle is used at 5, indicating that 5 is not included.

Front

When graphing the inequality x ≤ 3, what type of circle is used?

Back

A closed circle is used at 3, indicating that 3 is included.

Front

What is the solution to the inequality 84 - 4x ≤ 52?

Back

x > 8.

Front

What does the inequality x ≥ 4 mean on a number line?

Back

It represents all numbers greater than or equal to 4, shown with a closed circle at 4 and a line extending to the right.

Front

How do you graph the inequality x < -1?

Back

Use an open circle at -1 and shade to the left.

Front

What is the difference between an open circle and a closed circle in graphing inequalities?

Back

An open circle indicates that the number is not included (e.g., < or >), while a closed circle indicates that the number is included (e.g., ≤ or ≥).

Front

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

Back

x > 2.

Front

How do you represent the inequality -2x + 4 ≤ 10 on a number line?

Back

First, solve for x: -2x ≤ 6, so x ≥ -3. Graph with a closed circle at -3 and shade to the right.