Multi-Step Inequalities

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What is a multi-step inequality?

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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 on both sides.

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How do you isolate a variable in an inequality?

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To isolate a variable in an inequality, perform inverse operations on both sides of the inequality, similar to solving an equation, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

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What does it mean to graph the solution set of an inequality?

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Graphing the solution set of an inequality involves representing all possible solutions on a number line, using open or closed circles to indicate whether endpoints are included.

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What is the difference between a strict inequality and a non-strict inequality?

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A strict inequality (e.g., < or >) does not include the endpoint, while a non-strict inequality (e.g., ≤ or ≥) includes the endpoint.

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How do you solve the inequality -4a ≤ -28?

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To solve -4a ≤ -28, divide both sides by -4, which reverses the inequality sign, resulting in a ≥ 7.

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What is the solution to the inequality 4(2a + 3) < 3(a - 1)?

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To solve 4(2a + 3) < 3(a - 1), first distribute: 8a + 12 < 3a - 3. Then, subtract 3a from both sides: 5a + 12 < -3. Finally, subtract 12 and divide by 5 to get a < -3.

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

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Combine like terms: 14 < -4a + 6. Subtract 6 from both sides: 8 < -4a. Divide by -4 (reversing the inequality) to get a < -2.

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What is the solution to the inequality x ≤ -28/3?

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The solution x ≤ -28/3 indicates that x can take any value less than or equal to -28/3.

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

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Checking your solution in an inequality ensures that the values satisfy the original inequality, confirming that the solution is correct.

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What is the role of parentheses and brackets in graphing inequalities?

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Parentheses indicate that the endpoint is not included (open circle), while brackets indicate that the endpoint is included (closed circle) in the graph of the inequality.