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. For example, in the inequality 2x + 3 > 7, you would first subtract 3 and then divide by 2.

Front

How do you solve the inequality 7n - 1 > 76?

Back

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11.

Front

What does it mean to 'flip the sign' in an inequality?

Back

Flipping the sign means changing the direction of the inequality symbol (e.g., from > to <) when multiplying or dividing both sides by a negative number.

Front

When do you flip the sign in an inequality?

Back

You flip the sign when you multiply or divide both sides of the inequality by a negative number.

Front

What is the solution to the inequality 3x ≥ 12?

Back

Divide both sides by 3: x ≥ 4.

Front

What is the solution to the inequality -3x ≥ 12?

Back

Divide both sides by -3 (flip the sign): x ≤ -4.

Front

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

Back

Identify the quantities involved and express the relationship using an inequality symbol. For example, if Samantha has $22.50 and receives more money, you can write 22.50 + x > 32.

Front

What is the correct inequality for the situation: Samantha had $22.50 and now has more than $32.00?

Back

22.50 + x > 32.

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 performing the opposite operation (addition or subtraction) on both sides.

Front

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

Back

The second step is to isolate the variable by performing the remaining operation (multiplication or division) on both sides.