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 a compound inequality?

Back

In a compound inequality, 'and' indicates that both conditions must be true simultaneously.

Front

What does 'or' mean in a compound inequality?

Back

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

Front

How do you solve the compound inequality -3 ≤ 2x - 1 ≤ 5?

Back

Add 1 to all parts: -2 ≤ 2x ≤ 6. Then divide by 2: -1 ≤ x ≤ 3.

Front

What is the solution to the compound inequality 3x + 2 < -4 or 4x + 4 > 24?

Back

x < -2 or x > 5.

Front

How do you graph the compound inequality x ≥ 2 and x ≤ 4?

Back

Draw a number line, shade the region between 2 and 4, and include solid dots at 2 and 4.

Front

What is the difference between 'x > 2' and 'x ≥ 2'?

Back

'x > 2' means x is greater than 2 (not including 2), while 'x ≥ 2' means x is greater than or equal to 2 (including 2).

Front

What is the solution set for the compound inequality x < 1 or x > 3?

Back

The solution set includes all numbers less than 1 and all numbers greater than 3.

Front

How do you represent the solution of a compound inequality on a number line?

Back

Use open circles for '>' or '<' and closed circles for '≥' or '≤', shading the appropriate regions.

Front

What is the solution to the compound inequality 2x - 3 > 1 and x + 4 < 8?

Back

x > 2 and x < 4, which means 2 < x < 4.