Solving & 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

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

Back

Subtract 5 from all parts: 1 < x ≤ 6. This means x is greater than 1 and less than or equal to 6.

Front

Can x = 3 be a solution to the inequality 6 < x + 5 ≤ 11?

Back

Yes, because 3 satisfies the inequality.

Front

What does the inequality 0 < x + 7 < 9 represent?

Back

It represents two inequalities: -7 < x and x < 2.

Front

How do you model the scenario: Four times a number, increased by 6 is greater than 22?

Back

The inequality is 4x + 6 > 22.

Front

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

Back

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

Front

What must you do to the inequality when multiplying or dividing by a negative number?

Back

You must flip the inequality sign.

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 graph the compound inequality x < 2 or x > 5?

Back

You graph two separate regions: one to the left of 2 and one to the right of 5.

Front

What does the solution set of the inequality 4x + 6 > 22 look like?

Back

The solution set is x > 4.