Absolute Value Equations

Front

What is the definition of 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 the equation |x - a| = b?

Back

To solve |x - a| = b, you set up two equations: x - a = b and x - a = -b, then solve for x.

Front

What is the solution to the equation |x| = 0?

Back

The solution is x = 0.

Front

What does it mean if |x + 5| = -3?

Back

There is no solution because absolute values cannot be negative.

Front

How do you interpret the equation |x - 3| = 0 graphically?

Back

Graphically, it means that the point x = 3 is the only point where the distance from x to 3 is zero.

Front

What are the solutions to the equation |x| = c, where c > 0?

Back

The solutions are x = c and x = -c.

Front

How do you solve the equation |3x + 1| = 7?

Back

Set up two equations: 3x + 1 = 7 and 3x + 1 = -7, then solve for x.

Front

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

Back

The solution set is {3, -7}.

Front

What is the significance of the absolute value in real-world applications?

Back

Absolute value is used to represent quantities that cannot be negative, such as distance, speed, and magnitude.

Front

How do you solve the equation |2x - 4| = 8?

Back

Set up two equations: 2x - 4 = 8 and 2x - 4 = -8, then solve for x.