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

What does the phrase 'no more than' indicate in an inequality?

Back

The phrase 'no more than' indicates a less than or equal to relationship, represented by the symbol ≤.

Front

How do you solve the compound inequality 6 < x + 5 ≤ 11?

Back

First, isolate x: 6 < x + 5 means x > 1, and x + 5 ≤ 11 means x ≤ 6. The solution is 1 < x ≤ 6.

Front

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

Back

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

Front

What does the symbol '>' represent in an inequality?

Back

The symbol '>' represents 'greater than'.

Front

What does the symbol '<' represent in an inequality?

Back

The symbol '<' represents 'less than'.

Front

What does the symbol '≥' represent in an inequality?

Back

The symbol '≥' represents 'greater than or equal to'.

Front

What does the symbol '≤' represent in an inequality?

Back

The symbol '≤' represents 'less than or equal to'.

Front

How do you graph the inequality x ≤ -2 OR x > 5?

Back

Graph a solid dot at -2 and shade to the left, then graph an open dot at 5 and shade to the right.

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.