Solving Compound Inequalities

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What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'. It represents a range of values that satisfy all the inequalities involved.

Front

How do you solve a compound inequality with 'and'?

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To solve a compound inequality with 'and', you solve each inequality separately and then find the intersection of the solutions, which represents the values that satisfy both inequalities.

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How do you solve a compound inequality with 'or'?

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To solve a compound inequality with 'or', you solve each inequality separately and then combine the solutions, which represents the values that satisfy at least one of the inequalities.

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What does the solution x ≥ -5 and x < 4 represent?

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This solution represents all values of x that are greater than or equal to -5 and less than 4, forming a closed interval from -5 to 4.

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What is the first step in solving the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

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The first step is to isolate x in each inequality by performing algebraic operations such as addition, subtraction, multiplication, or division.

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What is the solution to the compound inequality -3 ≤ 2x - 1 ≤ 5?

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The solution is -1 ≤ x ≤ 3, meaning x can take any value from -1 to 3, inclusive.

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How do you express a budget constraint as an inequality?

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A budget constraint can be expressed as an inequality by setting the total expenses less than or equal to the budget limit. For example, if the budget is $1,400, the inequality would be total expenses ≤ $1,400.

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What does the inequality 700 + 125x ≤ 1,400 represent?

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This inequality represents the total budget for a team, where 700 is the fixed cost and 125x is the variable cost per day, ensuring the total does not exceed $1,400.

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

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In 'and' compound inequalities, both conditions must be true simultaneously, while in 'or' compound inequalities, at least one condition must be true.

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How do you graph the solution of x ≤ -2 OR x > 5?

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To graph this solution, shade the region to the left of -2 and the region to the right of 5 on a number line, indicating that x can take values in either of those ranges.