Compound and Linear Inequalities

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What is a compound inequality?

Back

A compound inequality is formed when two or more inequalities are combined into one statement by the words 'and' or 'or'. For example, x < 5 and x > 1.

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What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that a value can be less than or equal to another value.

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How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality sign, similar to solving an equation, while remembering to reverse the inequality sign if you multiply or divide by a negative number.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.

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What is the graph of an inequality?

Back

The graph of an inequality shows all the possible solutions on a number line or coordinate plane, often using a shaded region to indicate the solution set.

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What does the term 'solution' refer to in the context of inequalities?

Back

In the context of inequalities, a 'solution' refers to any value or set of values that satisfy the inequality.

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What is the difference between 'and' and 'or' in compound inequalities?

Back

In compound inequalities, 'and' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.

Front

How do you graph the inequality y ≤ -¾x - 1?

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To graph y ≤ -¾x - 1, first graph the line y = -¾x - 1 as a solid line (since it includes equality), then shade below the line to indicate all the values of y that satisfy the inequality.

Front

What is the meaning of the term 'boundary line' in inequalities?

Back

The boundary line is the line that represents the equation of the inequality. It divides the graph into two regions: one that satisfies the inequality and one that does not.

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What is the significance of the y-intercept in a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis. It helps in graphing the inequality and understanding the relationship between the variables.