Two-Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. It often involves addition or subtraction followed by multiplication or division.

Front

How do you solve a two-step inequality?

Back

1. Use addition or subtraction to move the constant term to the other side. 2. Use multiplication or division to isolate the variable. Remember to reverse the inequality sign if you multiply or divide by a negative number.

Front

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

Back

'≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

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

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

How can you represent a real-world situation with an inequality?

Back

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using an inequality.

Front

What is the first step in solving the inequality 3x + 5 < 20?

Back

Subtract 5 from both sides to isolate the term with the variable: 3x < 15.

Front

What is the solution to the inequality 2k - 4 ≥ 10?

Back

Add 4 to both sides to get 2k ≥ 14, then divide by 2 to find k ≥ 7.

Front

If you have the inequality 5x + 3 < 18, what is the value of x?

Back

First, subtract 3 from both sides: 5x < 15. Then divide by 5: x < 3.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values for the variable that can satisfy the inequality, often resulting from contradictory statements.

Front

How do you graph a two-step inequality on a number line?

Back

Draw a number line, plot the boundary point, and use an open circle for '<' or '>' and a closed circle for '≤' or '≥'. Shade the appropriate side based on the inequality.