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 k ≤ 7 mean in a real-world context?

Back

It means that the value of k can be any number less than or equal to 7, which could represent a limit or maximum in a real-world scenario.

Front

What is the first step to solve -3 − 6(4x + 6) > -111?

Back

Distribute -6: -3 - 24x - 36 > -111. Then combine like terms.

Front

What is the solution to the inequality 6x + 2 + 6x < 14?

Back

Combine like terms: 12x + 2 < 14. Then subtract 2 from both sides: 12x < 12, leading to x < 1.

Front

What does the inequality -4a ≤ -28 represent?

Back

It represents that the value of -4 times a is less than or equal to -28, which can be solved by dividing both sides by -4, reversing the inequality to a ≥ 7.

Front

What is the importance of reversing the inequality sign when dividing by a negative number?

Back

Reversing the inequality sign is crucial because it maintains the truth of the inequality when both sides are divided by a negative value.

Front

How can you graph the solution set of an inequality?

Back

To graph the solution set, plot a number line and use an open circle for < or > and a closed circle for ≤ or ≥, shading the appropriate direction.

Front

What does the solution x < 3 indicate?

Back

It indicates that x can take any value less than 3, which can be represented on a number line.

Front

What is the solution to the inequality a > -24?

Back

The solution indicates that a can be any number greater than -24.