3.5.5 Live Classroom: Solving and Graphing Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more inequalities using the words 'and' or 'or'.

Front

How do you solve the compound inequality 0 < x + 7 < 9?

Back

Subtract 7 from all parts: -7 < x < 2.

Front

What does 'and' mean in a compound inequality?

Back

It means that both conditions must be true simultaneously.

Front

What does 'or' mean in a compound inequality?

Back

It means that at least one of the conditions must be true.

Front

When solving inequalities, what must you do when multiplying or dividing by a negative number?

Back

You must flip the inequality sign.

Front

Solve the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22.

Back

x ≥ -5 and x < 4.

Front

Can x = -5 be a solution to the inequality -6 < 3x + 9 < 21?

Back

No.

Front

What is the solution set for the inequality x ≤ -2 OR x > 5?

Back

The solution set includes all numbers less than or equal to -2 and all numbers greater than 5.

Front

How do you graph the inequality x < 2?

Back

Draw a number line, place an open circle at 2, and shade to the left.

Front

What is the difference between 'x < 5' and 'x ≤ 5'?

Back

'x < 5' does not include 5, while 'x ≤ 5' includes 5.