Writing 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 represent a situation with an inequality?

Back

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

Front

What does the inequality symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

What does the inequality symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Front

How do you solve the inequality 10x + 300 ≥ 2000?

Back

Subtract 300 from both sides to get 10x ≥ 1700, then divide by 10 to find x ≥ 170.

Front

What is the first step in solving the inequality 2x + 5 < 3x?

Back

Subtract 2x from both sides to isolate the variable, resulting in 5 < x.

Front

How can you check if your solution to an inequality is correct?

Back

Substitute the solution back into the original inequality to see if it holds true.

Front

What is the solution to the inequality 7x - 25 ≥ 65?

Back

Add 25 to both sides to get 7x ≥ 90, then divide by 7 to find x ≥ 12.86.

Front

What does it mean if an inequality has no solution?

Back

It means that there is no value for the variable that can satisfy the inequality, often resulting in a contradiction.

Front

How do you graph the solution of an inequality on a number line?

Back

Use an open circle for '>' or '<' and a closed circle for '≥' or '≤', then shade the appropriate direction based on the inequality.