Solving Absolute Value Equations

Front

What is an absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation |A| = B, you set up two separate equations: A = B and A = -B.

Front

What is the solution set for |x| = 5?

Back

The solution set is {5, -5}.

Front

What does it mean if an absolute value equation has no solution?

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal the given value (e.g., |x| = -3 has no solution).

Front

Solve the equation |x - 3| = 7.

Back

The solutions are x = 10 and x = -4.

Front

What is the first step in solving |2x + 3| = 9?

Back

Set up two equations: 2x + 3 = 9 and 2x + 3 = -9.

Front

If |x + 4| = 0, what is x?

Back

x = -4.

Front

What is the graphical representation of an absolute value function?

Back

The graph of an absolute value function is a V-shape, opening upwards.

Front

Solve the equation |3x - 1| = 5.

Back

The solutions are x = 2 and x = -rac{4}{3}.

Front

What is the relationship between absolute value and distance?

Back

Absolute value represents the distance of a number from zero, and can also represent the distance between two points on a number line.