Absolute Value Equations-Retake

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

What does the equation |x - a| = b represent?

Back

This equation represents two possible equations: x - a = b or x - a = -b.

Front

How do you solve the equation |x - 3| = 5?

Back

Set up two equations: x - 3 = 5 and x - 3 = -5. Solve to find x = 8 or x = -2.

Front

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

Back

x = 2 or x = 8.

Front

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

Back

x = 8 or x = -2.

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, with the vertex at the point where the expression inside the absolute value equals zero.

Front

What is the relationship between absolute value and distance?

Back

Absolute value measures the distance of a number from zero, which can be interpreted as the distance between two points on a number line.

Front

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

Back

This means x can be either a or -a, as both have the same absolute value.

Front

What is the solution set for |x| = 4?

Back

x = 4 or x = -4.

Front

What happens when you have an absolute value equation set equal to a negative number?

Back

There are no solutions, as absolute values cannot be negative.