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 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 represent in a real-world context?

Back

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

Front

What is the first step in solving the inequality a − 6 ≤ 15 + 8a?

Back

Add 6 to both sides to isolate the variable term: a ≤ 21 + 8a.

Front

How do you isolate the variable in the inequality 6x + 2 < 14?

Back

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

Front

What does the solution x < 1 indicate?

Back

It means that x can take any value less than 1, which can be useful in determining ranges or limits.

Front

How do you solve the inequality -138 ≥ -6(6b − 7)?

Back

Distribute: -138 ≥ -36b + 42. Then, subtract 42 from both sides: -180 ≥ -36b, and divide by -36 (remember to flip the inequality): b ≥ 5.

Front

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

Back

Flipping the inequality sign is necessary because dividing or multiplying both sides of an inequality by a negative number reverses the order of the inequality.

Front

How do you solve the inequality 9 ≥ -2m + 2 − 3?

Back

Combine like terms: 9 ≥ -2m - 1. Then, add 1 to both sides: 10 ≥ -2m, and divide by -2 (flip the sign): m ≥ -5.

Front

What does the solution m ≥ -5 mean in a practical situation?

Back

It indicates that m can be any value greater than or equal to -5, which can represent a minimum threshold in a real-world context.