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, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 2x + 6 ≥ -8?

Back

Subtract 6 from both sides to get 2x ≥ -14, then divide by 2 to find x ≥ -7.

Front

What does the inequality symbol '≥' mean?

Back

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

Front

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

Back

Add 4 to both sides to get -3x < 9, then divide by -3 and flip the inequality to find x > -3.

Front

What happens to the inequality symbol when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol.

Front

What is the solution to the inequality 2 + 3x ≤ 20?

Back

Subtract 2 from both sides to get 3x ≤ 18, then divide by 3 to find x ≤ 6.

Front

What does the inequality symbol '<' mean?

Back

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

Front

How do you interpret the solution x < -20?

Back

The solution x < -20 means that any value less than -20 satisfies the inequality.

Front

What is the first step in solving a two-step inequality?

Back

The first step is usually to isolate the term with the variable by adding or subtracting a constant from both sides.

Front

What is the second step in solving a two-step inequality?

Back

The second step is to isolate the variable by multiplying or dividing both sides by a coefficient.