Absolute Value Test

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 an absolute value equation?

Back

To solve an equation of the form |A| = B, you set up two cases: A = B and A = -B, then solve for the variable.

Front

What is the solution to the equation |x - 3| = 5?

Back

x = 8 or x = -2.

Front

What does the equation |v + 8| - 5 = 2 represent?

Back

It represents the absolute value of (v + 8) being equal to 7, leading to two cases: v + 8 = 7 and v + 8 = -7.

Front

Solve the equation: |2x + 9| = 15.

Back

x = 3 or x = -12.

Front

What is the first step in solving the equation 6|1 - 5x| - 9 = 57?

Back

Add 9 to both sides to isolate the absolute value: 6|1 - 5x| = 66.

Front

What is the solution to the equation |n + 2| = 4?

Back

n = 2 or n = -6.

Front

How do you interpret the absolute value in the equation |x| = a?

Back

It means x can be either a or -a.

Front

What is the solution to the equation 9|9 - 2p| = 81?

Back

p = 0 or p = 9.

Front

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

Back

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