Solving 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

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

Back

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

Front

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

Back

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

Front

What does the inequality 0 < x + 7 < 9 represent?

Back

It represents two inequalities: x + 7 > 0 and x + 7 < 9, which can be solved to find the range of x.

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What is the solution to the inequality 24 > -3r > -9?

Back

The solution is -8 < r < 3.

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How do you graph the inequality x > 2?

Back

You draw a number line, place an open circle at 2, and shade to the right to indicate all numbers greater than 2.

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What does the inequality x ≤ -3 indicate?

Back

It indicates that x can be any number less than or equal to -3.

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What is the solution to the compound inequality 3x - 4 < -13 or 7x + 1 > 22?

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The solution is x < -3 or x > 3.

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

Back

'And' requires both conditions to be true simultaneously, while 'or' allows for either condition to be true.

Front

How do you isolate x in the inequality 3x - 4 < -13?

Back

Add 4 to both sides to get 3x < -9, then divide by 3 to find x < -3.