Multi-step Inequalities

Front

What is a multi-step inequality?

Back

A multi-step 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 28 - k ≥ 7(k - 4)?

Back

First, distribute: 28 - k ≥ 7k - 28. Then, combine like terms: 28 + 28 ≥ 7k + k. This simplifies to 56 ≥ 8k, or k ≤ 7.

Front

What does the solution a - 6 ≤ 15 + 8a represent?

Back

To solve, add 6 to both sides: a ≤ 21 + 8a. Then, subtract 8a from both sides: -7a ≤ 21, or a ≥ -3.

Front

What is the solution to the inequality 9 ≥ -2m + 2 - 3?

Back

Combine like terms: 9 ≥ -2m - 1. Add 1 to both sides: 10 ≥ -2m. Divide by -2 (remember to flip the inequality): m ≥ -5.

Front

How do you solve the inequality 3 < -5n + 2n?

Back

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

Front

What does the inequality 4(2a + 3) < 3(a - 1) represent?

Back

Distribute: 8a + 12 < 3a - 3. Subtract 3a from both sides: 5a + 12 < -3. Subtract 12: 5a < -15, or a < -3.

Front

What is the importance of flipping the inequality sign when multiplying or 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 first step in solving a multi-step inequality?

Back

The first step is to simplify both sides of the inequality, which may involve distributing, combining like terms, or moving constants.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution when the variable cannot satisfy the inequality, such as when it leads to a false statement like 5 < 3.

Front

What is the graphical representation of an inequality?

Back

The graphical representation of an inequality shows a number line with an open or closed circle at the boundary point, indicating whether the endpoint is included.