Solving Two-Step Linear Inequalities

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What is a two-step linear inequality?

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A two-step linear inequality is an inequality that requires two operations to isolate the variable. It typically takes the form of ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c.

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How do you solve a two-step linear inequality?

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To solve a two-step linear inequality, perform the following steps: 1) Use addition or subtraction to move the constant term to the other side of the inequality. 2) Use multiplication or division to isolate the variable. Remember to reverse the inequality sign if you multiply or divide by a negative number.

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What does it mean to reverse the inequality sign?

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Reversing the inequality sign means changing the direction of the inequality. For example, if you have x < 5 and you multiply both sides by -1, it becomes -x > -5.

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What is the difference between < and ≤?

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The symbol < means 'less than' and does not include the value, while ≤ means 'less than or equal to' and includes the value.

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What is the solution set of an inequality?

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The solution set of an inequality is the set of all values that satisfy the inequality. It can be represented on a number line or in interval notation.

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How do you graph a two-step linear inequality?

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To graph a two-step linear inequality, first graph the corresponding equation as a line. Use a solid line for ≤ or ≥ and a dashed line for < or >. Then shade the region that represents the solution set.

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What is an example of a two-step linear inequality?

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An example of a two-step linear inequality is 2x + 3 < 7.

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How do you check your solution for a two-step linear inequality?

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

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What is the importance of inequalities in real life?

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Inequalities are important in real life as they help in making decisions based on constraints, such as budgeting, resource allocation, and comparing quantities.

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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 can satisfy it. For example, x < x is always false.