Multi-Step & Compound Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does interval notation represent?

Back

Interval notation is a way of writing subsets of the real number line using intervals, indicating the lower and upper bounds and whether they are included (closed) or excluded (open).

Front

How do you express the solution x > 3 in interval notation?

Back

(3, ∞)

Front

What is the solution to the inequality 2x + 4 < 12?

Back

x < 4

Front

How do you solve the compound inequality 1 < 2x + 3 < 7?

Back

1 < 2x + 3 < 7 can be solved by breaking it into two parts: 1 < 2x + 3 and 2x + 3 < 7. The solution is -1 < x < 2.

Front

What does the symbol '∪' represent in interval notation?

Back

The symbol '∪' represents the union of two sets, meaning all elements that are in either set.

Front

How do you express the solution x ≤ 5 in interval notation?

Back

(-∞, 5]

Front

What is the solution to the inequality 3x - 5 ≥ 4?

Back

x ≥ 3.

Front

What does the term 'compound inequality' mean?

Back

A compound inequality combines two inequalities, often connected by 'and' or 'or', to express a range of values.

Front

How do you express the solution x < -2 or x > 3 in interval notation?

Back

(-∞, -2) ∪ (3, ∞)