Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you represent the solution to the inequality 5w ≥ 30 on a number line?

Back

You would shade to the right of 6 (since w ≥ 6) and use a closed dot at 6.

Front

What is the first step to solve the inequality 4x + 1 > 13?

Back

Subtract 1 from both sides to get 4x > 12.

Front

What do you do after isolating the variable in an inequality?

Back

You divide or multiply both sides by the same number, but remember to flip the inequality sign if you multiply or divide by a negative.

Front

When do you use an open dot on a number line?

Back

An open dot is used when the inequality symbol is < or >, indicating that the endpoint is not included.

Front

What is the solution to the inequality x > 3?

Back

Any number greater than 3 is a solution.

Front

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

Back

You would shade to the left of 2 and use a closed dot at 2.

Front

What is the solution to the inequality 0.75n + 1.75 ≤ 20?

Back

Subtract 1.75 from both sides to get 0.75n ≤ 18.25, then divide by 0.75 to find n ≤ 24.33.