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 'x > 2 or x ≤ -3' represent?

Back

This represents two separate conditions: x is greater than 2, or x is less than or equal to -3.

Front

How do you solve the compound inequality -3 < 3x < 6?

Back

Divide all parts by 3: -1 < x < 2.

Front

What is the solution to the inequality x + 2 < -4?

Back

Subtract 2 from both sides: x < -6.

Front

What does the graph of -2 ≤ x ≤ 5 look like?

Back

It includes all numbers from -2 to 5, including -2 and 5.

Front

What is the solution to the compound inequality -5x < -15?

Back

Divide by -5 (remember to flip the inequality): x > 3.

Front

How do you graph the inequality x < -2 or x > 5?

Back

Draw a number line with open circles at -2 and 5, shading to the left of -2 and to the right of 5.

Front

What does the inequality 7 < x < 12 mean?

Back

It means x is greater than 7 and less than 12.

Front

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

Back

'And' means both conditions must be true, while 'or' means at least one condition must be true.

Front

How do you solve the compound inequality x + 2 < -4 or -5x < -15?

Back

Solve each inequality separately: x < -6 or x > 3.