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 solve a compound inequality with 'and'?

Back

To solve a compound inequality with 'and', find the intersection of the solution sets of the individual inequalities.

Front

How do you solve a compound inequality with 'or'?

Back

To solve a compound inequality with 'or', find the union of the solution sets of the individual inequalities.

Front

What does the notation 'a < x < b' represent?

Back

It represents that x is greater than a and less than b.

Front

Solve the compound inequality: -3 < 2x + 1 < 5.

Back

-2 < x < 2.

Front

What is the solution to the inequality: 0 < x + 7 < 9?

Back

-7 < x < 2.

Front

How do you graph a compound inequality with 'and'?

Back

Shade the region where both inequalities overlap on a number line.

Front

How do you graph a compound inequality with 'or'?

Back

Shade the regions of both inequalities separately on a number line.

Front

What is the solution to the inequality: -8 < 2(x + 4) or -3x + 4 > x - 4?

Back

x < -8 or x < 2.

Front

What does 'x ≤ -2 AND x > 5' imply?

Back

This compound inequality has no solution because no number can satisfy both conditions simultaneously.