Solving Absolute Value Equations

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

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

Back

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

Front

What does the equation |x + 5| = 3 represent?

Back

It represents two equations: x + 5 = 3 and x + 5 = -3, leading to solutions x = -2 and x = -8.

Front

What is the first step in solving |6 - 2k| = 18?

Back

The first step is to set up two separate equations: 6 - 2k = 18 and 6 - 2k = -18.

Front

What are the solutions to the equation |x + 10| = 11?

Back

The solutions are x + 10 = 11 (x = 1) and x + 10 = -11 (x = -21), so x = 1 and x = -21.

Front

How do you interpret the absolute value |x|?

Back

The absolute value |x| is the non-negative value of x, meaning it is always zero or positive.

Front

What is the solution set for the equation |x| = 0?

Back

The solution set is {0}, since the only number whose absolute value is zero is zero itself.

Front

What does the equation |x - 4| = 5 represent?

Back

It represents two equations: x - 4 = 5 and x - 4 = -5, leading to solutions x = 9 and x = -1.

Front

What is the solution to the equation |x/4| = 8?

Back

The solutions are x/4 = 8 (x = 32) and x/4 = -8 (x = -32), so x = 32 and x = -32.

Front

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

Back

Absolute value is used to represent quantities that cannot be negative, such as distance, temperature differences, and financial losses.