Solving Multistep Inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality 6x + 2 < 14?

Back

Subtract 2 from both sides: 6x < 12. Then divide by 6: x < 2.

Front

What is the solution to the inequality 7(x + 3) < 5x + 13?

Back

Distribute: 7x + 21 < 5x + 13. Subtract 5x from both sides: 2x + 21 < 13. Subtract 21: 2x < -8. Divide by 2: x < -4.

Front

What does it mean if an inequality has no solution?

Back

It means that there are no values for the variable that can satisfy the inequality.

Front

What does it mean if an inequality has infinite solutions?

Back

It means that any value for the variable will satisfy the inequality.

Front

How do you solve the inequality -3 - 6(4x + 6) > -111?

Back

Distribute: -3 - 24x - 36 > -111. Combine like terms: -24x - 39 > -111. Add 39: -24x > -72. Divide by -24 (reverse the inequality): x < 3.

Front

What is the solution to the inequality 3 < -5n + 2n?

Back

Combine like terms: 3 < -3n. Divide by -3 (reverse the inequality): n < -1.

Front

What is the first step in solving a multistep inequality?

Back

Identify and isolate the variable by performing inverse operations.

Front

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

Back

The inequality sign reverses direction.

Front

What is the importance of checking your solution in an inequality?

Back

To ensure that the solution satisfies the original inequality and to verify its correctness.