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 the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'.

Front

How do you solve the compound inequality -13 < 2x + 5 < 15?

Back

First, isolate 2x: -18 < 2x < 10. Then divide by 2: -9 < x < 5.

Front

What is the solution set for the inequality 6 > x?

Back

The solution set is all real numbers less than 6.

Front

What does 'x ≥ -2 OR x < 5' represent graphically?

Back

It represents all values of x that are either greater than or equal to -2 or less than 5.

Front

What is the solution to the inequality -4x + 1 ≤ 21?

Back

x ≥ -5.

Front

What is the solution to the inequality 5x + 2 < 22?

Back

x < 4.

Front

What is the final solution set for the compound inequality x ≥ -5 and x < 4?

Back

The solution set is -5 ≤ x < 4.

Front

What does the solution 'All real numbers' mean in the context of inequalities?

Back

It means that any value of x satisfies the inequality.