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 25 < X - 10?

Back

To solve 25 < X - 10, add 10 to both sides to get 35 < X, which can be rewritten as X > 35.

Front

What is the first step in solving the inequality 22 < 6c + 4?

Back

The first step is to subtract 4 from both sides, resulting in 18 < 6c.

Front

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

Back

After isolating the variable, you may need to divide or multiply both sides by a number, remembering to flip the inequality sign if you multiply or divide by a negative number.

Front

When solving -3x ≥ 12, what should you do first?

Back

First, divide both sides by -3, which requires flipping the inequality sign, resulting in x ≤ -4.

Front

What does an open circle represent when graphing inequalities?

Back

An open circle represents that the number is not included in the solution set, indicating that the inequality is strict (e.g., < or >).

Front

What does a closed circle represent when graphing inequalities?

Back

A closed circle represents that the number is included in the solution set, indicating that the inequality is non-strict (e.g., ≤ or ≥).

Front

How do you graph the inequality b < 6?

Back

To graph b < 6, place an open circle on 6 and shade to the left, indicating all values less than 6.

Front

What is the solution to the inequality s + 9 ≥ -25?

Back

To solve s + 9 ≥ -25, subtract 9 from both sides to get s ≥ -34.

Front

What is the importance of flipping the inequality sign?

Back

Flipping the inequality sign is crucial when multiplying or dividing both sides of an inequality by a negative number, as it changes the direction of the inequality.