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 symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you express the solution of an inequality in interval notation?

Back

In interval notation, the solution is expressed as a range of values, using parentheses for exclusive bounds and brackets for inclusive bounds.

Front

Solve the compound inequality: 2 < x + 3 < 7

Back

The solution is -1 < x < 4.

Front

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

Back

The solution is -3 ≤ x < 1.

Front

What is the solution set for the inequality: x < 4 or x > 10?

Back

The solution set is (-∞, 4) ∪ (10, ∞).

Front

How do you graph a compound inequality on a number line?

Back

To graph a compound inequality, shade the regions that represent the solution set on a number line.