Multistep Inequalities

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What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

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How do you isolate a variable in a multistep inequality?

Back

To isolate a variable in a multistep inequality, perform inverse operations in the reverse order of operations, ensuring to maintain the inequality's direction when multiplying or dividing by a negative number.

Front

What is the importance of reversing the inequality sign?

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The inequality sign must be reversed when both sides of the inequality are multiplied or divided by a negative number to maintain the truth of the inequality.

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What does the solution x ≤ -11 represent on a number line?

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The solution x ≤ -11 represents all numbers less than or equal to -11, which can be shown on a number line with a closed circle at -11 and a line extending to the left.

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What are the steps to solve the inequality 3x - 5 > 4?

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1. Add 5 to both sides: 3x > 9. 2. Divide both sides by 3: x > 3.

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How do you check the solution of an inequality?

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To check the solution of an inequality, substitute a value from the solution set back into the original inequality to see if it holds true.

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What is the difference between an equation and an inequality?

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An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

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What does it mean if an inequality has no solution?

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An inequality has no solution if there are no values that satisfy the inequality, often represented by a contradiction such as 5 < 3.

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What is a compound inequality?

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A compound inequality consists of two or more inequalities joined by 'and' or 'or', representing a range of values.

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How do you graph a compound inequality?

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To graph a compound inequality, graph each inequality on the same number line and identify the overlapping or combined regions based on whether it is 'and' or 'or'.