Compound Inequalities and Absolute Value Inequalities Review

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'and' or 'or'. For example, x < 5 and x > 2.

Front

What does the symbol '|' represent in absolute value inequalities?

Back

The symbol '|' represents the absolute value, which measures the distance of a number from zero on the number line.

Front

How do you solve an absolute value inequality like |x| < a?

Back

To solve |x| < a, split it into two inequalities: -a < x < a.

Front

What is the solution to the inequality -5|x - 4| > 20?

Back

No solution, because the absolute value cannot be negative.

Front

What does 'or' mean in compound inequalities?

Back

'Or' means that at least one of the inequalities must be true for the solution to be valid.

Front

How do you solve a compound inequality like 3x + 2 < -4 or 4x + 4 > 24?

Back

Solve each inequality separately: x < -2 or x > 5.

Front

What is the solution to the inequality -3 ≤ 2x - 1 ≤ 5?

Back

The solution is -1 ≤ x ≤ 3.

Front

How do you write an inequality for the graph showing all numbers between -2 and 5?

Back

The inequality is -2 ≤ x ≤ 5.

Front

What is the solution to the inequality 3|2d + 9| + 13 > 10?

Back

All real numbers, because the absolute value expression can take any value.

Front

What does 'and' mean in compound inequalities?

Back

'And' means that both inequalities must be true for the solution to be valid.