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'. For example, x > 1 and x < 5.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that a value can be either less than or equal to another value.

Front

How do you graph the compound inequality -2 ≤ x ≤ 3?

Back

To graph -2 ≤ x ≤ 3, draw a number line, shade the region between -2 and 3, and use closed circles at -2 and 3 to indicate that these endpoints are included.

Front

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

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.

Front

Solve the compound inequality 2 ≤ 4x - 14 ≤ 10.

Back

First, solve the inequalities separately: 2 ≤ 4x - 14 gives x ≥ 4, and 4x - 14 ≤ 10 gives x ≤ 6. Therefore, the solution is 4 ≤ x ≤ 6.

Front

What does the graph of x > 1 look like?

Back

The graph of x > 1 is represented by a number line with an open circle at 1 and shading to the right, indicating all values greater than 1.

Front

How do you represent the solution for x < 1 or x > 4?

Back

The solution is represented on a number line with an open circle at 1 and 4, shading to the left of 1 and to the right of 4.

Front

What is the solution set for the compound inequality x > 1 and x > 4?

Back

The solution set is x > 4, since both conditions must be true, and the more restrictive condition is x > 4.

Front

How do you solve the compound inequality 3 < x + 2 < 7?

Back

First, solve the inequalities separately: 3 < x + 2 gives x > 1, and x + 2 < 7 gives x < 5. Therefore, the solution is 1 < x < 5.

Front

What does the graph of x ≤ 3 look like?

Back

The graph of x ≤ 3 is represented by a number line with a closed circle at 3 and shading to the left, indicating all values less than or equal to 3.