Solving Two-Step Linear Inequalities

Front

What is a two-step linear inequality?

Back

A two-step linear inequality is an inequality that can be solved in two steps, involving operations such as addition, subtraction, multiplication, or division to isolate the variable.

Front

How do you solve the inequality 2x + 3 < 11?

Back

Step 1: Subtract 3 from both sides: 2x < 8. Step 2: Divide both sides by 2: x < 4.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left is larger than the value on the right.

Front

What is the solution set of the inequality x + 5 > 10?

Back

The solution set is x > 5.

Front

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

Back

Draw an open circle at 3 and shade to the left to indicate all numbers less than 3.

Front

What is the difference between an open circle and a closed circle on a number line?

Back

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

Front

How do you solve the inequality 3x - 4 ≥ 5?

Back

Step 1: Add 4 to both sides: 3x ≥ 9. Step 2: Divide both sides by 3: x ≥ 3.

Front

What is a compound inequality?

Back

A compound inequality consists of two inequalities joined by 'and' or 'or', representing a range of values.

Front

How do you solve the compound inequality 1 < 2x + 3 < 7?

Back

Step 1: Solve 1 < 2x + 3: 2x > -2, so x > -1. Step 2: Solve 2x + 3 < 7: 2x < 4, so x < 2. The solution is -1 < x < 2.