Solving Absolute Value Equations

Front

What is the definition of absolute value?

Back

The absolute value of a number is the distance of that number from zero on the number line, regardless of direction.

Front

How do you solve the equation |x - 3| = 40?

Back

To solve |x - 3| = 40, set up two equations: x - 3 = 40 and x - 3 = -40. Solving these gives x = 43 and x = -37.

Front

Why is absolute value always a positive number?

Back

Absolute value represents distance, and distance is always measured as a non-negative quantity.

Front

Evaluate the expression |1 - 5|.

Back

|1 - 5| = |-4| = 4.

Front

Evaluate the expression |-2| + |-5|.

Back

|-2| + |-5| = 2 + 5 = 7.

Front

What are the two cases to consider when solving an absolute value equation?

Back

When solving |A| = B, consider the cases A = B and A = -B.

Front

If |x| = 0, what is the value of x?

Back

If |x| = 0, then x = 0.

Front

What is the geometric interpretation of absolute value?

Back

The absolute value of a number represents its distance from zero on the number line.

Front

How do you graph the equation |x| = a?

Back

To graph |x| = a, plot two vertical lines at x = a and x = -a.

Front

What is the solution set for the equation |x + 2| = 5?

Back

The solution set is x = 3 and x = -7.