Absolute value equation FLASHCARD per 6

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, always expressed as a positive value.

Front

Solve the equation: 5|x| - 8 = 2

Back

x = 2, x = -2

Front

Evaluate the expression: |x + 9| = -5

Back

No solution, because absolute values cannot be negative.

Front

Solve the equation: |x – 12| - 3 = 11

Back

x = 26, x = -2

Front

Why is absolute value always positive?

Back

Absolute value measures distance from zero, and distance is always a positive quantity.

Front

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

Back

It represents two possible equations: v + 8 = 7 and v + 8 = -7, leading to solutions v = -1 and v = -15.

Front

If |x| = a, what can we conclude about x?

Back

x can be either a or -a.

Front

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

Back

The solution set is {0}.

Front

How do you graph absolute value functions?

Back

Absolute value functions create a V-shape on the graph, opening upwards.

Front

What is the general form of an absolute value equation?

Back

The general form is |ax + b| = c, where a, b, and c are constants.