Pd 5 Absolute value equation FLASHCARD

Front

What is an 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 absolute value equation, isolate the absolute value expression and then create two separate equations: one for the positive case and one for the negative case.

Front

What is the first step in solving the equation |x - 3| + 2 = 6?

Back

Isolate the absolute value expression by subtracting 2 from both sides: |x - 3| = 4.

Front

Solve the equation |2x - 3| + 5 = 10.

Back

The solutions are x = -1 and x = 4.

Front

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

Back

It represents the absolute value of (v + 8) being equal to 7 or -3, leading to two possible equations.

Front

What are the solutions to the equation |x - 12| - 3 = 11?

Back

The solutions are x = 26 and x = -2.

Front

What is the solution set for the equation -2|−2r − 4| = -12?

Back

The solution set is {-5, 1}.

Front

What does it mean if an absolute value equation has no solution?

Back

It means that there are no values for the variable that can satisfy the equation.

Front

How do you graph an absolute value function?

Back

An absolute value function forms a V-shape on the graph, with the vertex at the point where the expression inside the absolute value equals zero.

Front

What is the geometric interpretation of absolute value?

Back

The absolute value represents the distance from a point to the origin on a number line.