Solving and Graphing 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 'and' mean in a compound inequality?

Back

In a compound inequality, 'and' means that both conditions must be true at the same time.

Front

What does 'or' mean in a compound inequality?

Back

In a compound inequality, 'or' means that at least one of the conditions must be true.

Front

How do you solve the compound inequality -3 ≤ 2x - 1 ≤ 5?

Back

Add 1 to all parts: -2 ≤ 2x ≤ 6, then divide by 2: -1 ≤ x ≤ 3.

Front

What is the solution to the inequality 0 < x + 7 < 9?

Back

The solution is -7 < x < 2.

Front

When do you flip the inequality sign?

Back

You flip the inequality sign when you multiply or divide both sides of the inequality by a negative number.

Front

What is the solution to the inequality x > 2 or x ≤ -3?

Back

The solution includes all values greater than 2 and all values less than or equal to -3.

Front

How do you graph the inequality 2 ≤ x ≤ 4?

Back

You draw a number line, shade between 2 and 4, and use closed circles at 2 and 4.

Front

What is the difference between 'x > 2' and 'x ≥ 2'?

Back

'x > 2' means x is greater than 2 (not including 2), while 'x ≥ 2' means x is greater than or equal to 2 (including 2).

Front

What is the solution to the inequality x < 4 and x > 2?

Back

The solution is 2 < x < 4.