Solving and Graphing Multistep Inequalities

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What is a multistep inequality?

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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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What does it mean to graph an inequality?

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Graphing an inequality involves representing the solutions of the inequality on a number line or coordinate plane, using a solid line for 'greater than or equal to' and 'less than or equal to', and a dashed line for 'greater than' and 'less than'.

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What is the difference between '>' and '≥'?

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'>' means greater than, while '≥' means greater than or equal to. The latter includes the boundary value in the solution set.

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What is the first step in solving a multistep inequality?

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The first step is to isolate the variable term on one side of the inequality, often by adding or subtracting constants.

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How do you handle inequalities when multiplying or dividing by a negative number?

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When multiplying or dividing both sides of an inequality by a negative number, you must flip the direction of the inequality sign.

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The solution set includes all real numbers less than 5, which can be represented on a number line with an open circle at 5.

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What does the term 'solution set' refer to?

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The solution set refers to all the values that satisfy the inequality.

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How can you check if a number is a solution to an inequality?

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To check if a number is a solution, substitute it into the inequality and see if the statement is true.

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What is the significance of the boundary point in an inequality?

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The boundary point is the value that separates the solution set from non-solution values. It is included in the solution set if the inequality is '≤' or '≥'.