Alg 1 Ch 2.5-2.7: Solving 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 the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 2 means x is greater than 2.

Front

What does the symbol '<' mean in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 5 means x is less than 5.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 3 means x is greater than or equal to 3.

Front

What does the symbol '≤' mean in inequalities?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x is less than or equal to 4.

Front

How do you solve a simple inequality like x + 3 > 5?

Back

Subtract 3 from both sides: x > 2.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, such as x > 1 and x < 5, often written as 1 < x < 5.

Front

How do you graph the inequality x > 2?

Back

Draw a number line, place an open circle at 2, and shade to the right to indicate all numbers greater than 2.

Front

What is the first step in solving |x - 3| < 5?

Back

Split into two inequalities: x - 3 < 5 and x - 3 > -5.

Front

What is the solution to the inequality -3 < 2x + 1 < 5?

Back

Subtract 1 from all parts: -4 < 2x < 4, then divide by 2: -2 < x < 2.