Compound Inequalities

Front

What is a compound inequality?

Back

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

Front

What does the symbol |x| represent?

Back

The symbol |x| represents the absolute value of x, which is the distance of x from 0 on the number line.

Front

How do you solve the equation |2x - 1| = 7?

Back

Set up two equations: 2x - 1 = 7 and 2x - 1 = -7. Solve to find x = 4 and x = -3.

Front

What is the solution to the inequality |x + 3| > 8?

Back

The solution is x > 5 or x < -11.

Front

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

Back

Draw a number line, shade the region between -2 and 5, and use closed circles at -2 and 5.

Front

What does the inequality x > 2 mean?

Back

It means that x can take any value greater than 2.

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 < -3 or x > 2?

Back

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

Front

What is the solution to the inequality |x - 4| < 3?

Back

The solution is 1 < x < 7.

Front

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

Back

It is a number line with a closed circle at -2 and shading to the left.