Sec. 4-4 PII 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 solve the inequality -3x - 4 < 5?

Back

Add 4 to both sides: -3x < 9. Then divide by -3 (remember to flip the inequality): x > -3.

Front

What does the solution x > -3 represent on a number line?

Back

It represents all numbers greater than -3, extending to the right on the number line.

Front

How do you solve the inequality -4a + 16 > 8?

Back

Subtract 16 from both sides: -4a > -8. Then divide by -4 (flip the inequality): a < 2.

Front

What does the solution a < 2 indicate?

Back

It indicates that a can be any number less than 2.

Front

How do you solve the inequality 7k - 2 ≥ -9?

Back

Add 2 to both sides: 7k ≥ -7. Then divide by 7: k ≥ -1.

Front

What does the solution k ≥ -1 mean?

Back

It means k can be -1 or any number greater than -1.

Front

How do you solve the inequality 22 < 6c + 4?

Back

Subtract 4 from both sides: 18 < 6c. Then divide by 6: 3 < c or c > 3.

Front

What is the significance of flipping the inequality sign when dividing by a negative number?

Back

Flipping the inequality sign ensures that the relationship between the two sides of the inequality remains true.

Front

What is the general form of a two-step inequality?

Back

The general form is ax + b < c or ax + b > c, where a, b, and c are constants.