Compound Inequalities

Front

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'.

Front

What does 'and' mean in a compound inequality?

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In a compound inequality, 'and' means that both conditions must be true at the same time.

Front

What does 'or' mean in a compound inequality?

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In a compound inequality, 'or' means that at least one of the conditions must be true.

Front

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

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To solve a compound inequality with 'and', find the intersection of the solution sets of the individual inequalities.

Front

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

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To solve a compound inequality with 'or', find the union of the solution sets of the individual inequalities.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) or [a, b].

Front

How do you express the solution set x ≥ -5 and x < 4 in interval notation?

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The solution set x ≥ -5 and x < 4 is expressed in interval notation as [-5, 4).

Front

What is the graphical representation of the inequality -8 ≤ x < 8?

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The graphical representation includes a solid dot at -8 and an open dot at 8, with a line connecting them.

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What is the solution to the compound inequality x < 1 and x > 5?

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The solution is 'No Solution' because there are no numbers that satisfy both conditions simultaneously.

Front

What is the solution to the compound inequality x < 1 or x > 5?

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The solution includes all numbers less than 1 and all numbers greater than 5.