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 operations such as addition, subtraction, multiplication, or division.

Front

How do you solve the inequality x/2 - 6 < -8?

Back

Add 6 to both sides: x/2 < -2. Then multiply both sides by 2: x < -4.

Front

What does the inequality 5x + 3 ≥ 18 represent?

Back

To solve, subtract 3 from both sides: 5x ≥ 15. Then divide by 5: x ≥ 3.

Front

What is the solution to the inequality 28 - k ≥ 7(k - 4)?

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Distribute: 28 - k ≥ 7k - 28. Combine like terms: 56 ≥ 8k, or k ≤ 7.

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How do you graph the inequality x/3 - 2 < 4?

Back

First, solve for x: x/3 < 6, then x < 18. Graph with an open circle at 18 and shade left.

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What does the inequality 9 ≥ -2m + 2 - 3 mean?

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To solve, simplify: 9 ≥ -2m - 1. Then add 1: 10 ≥ -2m, or m ≥ -5.

Front

What is the meaning of the symbol '≥'?

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The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

How do you interpret the solution k ≤ 7?

Back

This means that k can be any number less than or equal to 7.

Front

What is the first step in solving the inequality 4(b + 3) - 6 ≤ -2?

Back

First, add 6 to both sides: 4(b + 3) ≤ 4.

Front

What does the solution m ≥ 5 indicate?

Back

This indicates that m can be any number greater than or equal to 5.