Solving and Graphing 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 'and' mean in compound inequalities?

Back

In compound inequalities, 'and' indicates that both conditions must be true at the same time.

Front

What does 'or' mean in compound inequalities?

Back

In compound inequalities, 'or' indicates that at least one of the conditions must be true.

Front

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

Back

1. Solve each inequality separately: 3x < -6 (x < -2) and 4x > 20 (x > 5). 2. Combine the solutions: x < -2 or x > 5.

Front

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

Back

The solution is -1 ≤ x ≤ 3.

Front

How do you graph the inequality x > 2 or x ≤ -3?

Back

Graph a dashed line at x = 2 and shade to the right. Graph a solid line at x = -3 and shade to the left.

Front

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

Back

No, substituting x = -5 gives -6 < -6 < 21, which is false.

Front

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

Back

'And' requires both conditions to be true, while 'or' requires at least one condition to be true.

Front

How do you check if a number is a solution to a compound inequality?

Back

Substitute the number into the compound inequality and see if the resulting statement is true.

Front

What is the graphical representation of 2 ≤ x ≤ 4?

Back

A solid line at x = 2 and x = 4 with shading between the two lines.