Solving 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 represent the compound inequality 'x < 5 and x > -2' on a number line?

Back

You would shade the region between -2 and 5, not including -2 and 5.

Front

What happens to the inequality sign when you multiply or divide both sides of an inequality by a negative number?

Back

The inequality sign must be flipped.

Front

Solve the compound inequality: -3 ≤ 2x - 1 ≤ 5. What is the solution set?

Back

The solution set is -1 ≤ x ≤ 3.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.

Front

How do you solve the compound inequality 3x - 4 < -13 or 7x + 1 > 22?

Back

First, solve each inequality separately: x < -3 or x > 3.

Front

What is the graphical representation of the inequality 6 > x?

Back

It is represented by shading to the left of 6 on a number line, not including 6.

Front

What does the solution 'x < -3 or x > 3' indicate about the values of x?

Back

It indicates that x can be any value less than -3 or any value greater than 3.

Front

What is the first step in solving a compound inequality?

Back

Isolate the variable in the middle of the compound inequality.

Front

When given a compound inequality, how do you check your solution?

Back

Substitute values from the solution set back into the original inequalities to see if they hold true.