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'.

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What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' indicates that at least one of the inequalities must be true for the solution to be valid.

Front

What does 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' indicates that both inequalities must be true for the solution to be valid.

Front

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

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To solve a compound inequality with 'or', solve each inequality separately and combine the solutions.

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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 solutions of the individual inequalities.

Front

What is the solution to the inequality 3x - 4 < -13?

Back

x < -3.

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What is the solution to the inequality 7x + 1 > 22?

Back

x > 3.

Front

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

Back

x < -3 or x > 3.

Front

What is the solution to the compound inequality -8 < 2(x + 4) or -3x + 4 > x - 4?

Back

x > -8 or x < 2.

Front

How do you graph the solution of a compound inequality?

Back

Graph each inequality on the number line and shade the appropriate regions based on 'and' or 'or'.