Inequalities and Absolute Value Equations

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or equal to the other. Examples include <, >, ≤, and ≥.

Front

What does the symbol '<' represent?

Back

The symbol '<' means 'less than'. For example, if x < 5, it means x is any number less than 5.

Front

What does the symbol '>' represent?

Back

The symbol '>' means 'greater than'. For example, if x > 3, it means x is any number greater than 3.

Front

How do you solve the inequality 4 - 2x < 14?

Back

First, subtract 4 from both sides: -2x < 10. Then, divide by -2 (remember to flip the inequality): x > -5.

Front

What does the solution x > -5 mean on a number line?

Back

It means that all numbers to the right of -5 (not including -5) are solutions to the inequality.

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, such as |x| = a, where a is a non-negative number.

Front

What does the equation |2x - 1| = -5 imply?

Back

Since absolute values cannot be negative, this equation has no solution.

Front

What is the first step to solve |x| = a?

Back

Set up two equations: x = a and x = -a.

Front

What does the solution x ≤ 4 mean?

Back

It means that x can be any number less than or equal to 4.

Front

How do you interpret the number line for x < -4?

Back

The number line shows all numbers to the left of -4 (not including -4 itself) as solutions.