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 graph a compound inequality using 'and'?

Back

To graph a compound inequality using 'and', find the intersection of the solution sets of the individual inequalities and shade that region on the number line.

Front

How do you graph a compound inequality using 'or'?

Back

To graph a compound inequality using 'or', find the union of the solution sets of the individual inequalities and shade both regions on the number line.

Front

What does the symbol '<' represent in inequalities?

Back

The symbol '<' means 'less than' and indicates that the value on the left is smaller than the value on the right.

Front

What does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to' and indicates that the value on the left is smaller than or equal to the value on the right.

Front

How do you solve the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

First, solve each inequality separately: -4x ≤ 20 gives x ≥ -5, and 5x < 20 gives x < 4. The final solution set is x ≥ -5 and x < 4.

Front

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

Back

The solution set is x < -8 or x < 2.

Front

What does it mean if a solution set is 'all real numbers'?

Back

If a solution set is 'all real numbers', it means that any real number satisfies the inequality.

Front

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

Back

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

Front

How do you combine inequalities when using 'and'?

Back

When using 'and', you combine the inequalities by finding the overlap of the solution sets.