Absolute Value Equations

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 absolute value equation, set the expression inside the absolute value equal to both the positive and negative values of the other side of the equation.

Front

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

Back

x = 8 or x = 2.

Front

What does the equation |x| = a imply when a < 0?

Back

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

Front

What is the solution to the equation |2x + 1| = 5?

Back

x = 2 or x = -3.

Front

How do you isolate the absolute value in an equation?

Back

To isolate the absolute value, move all other terms to the opposite side of the equation.

Front

What is the solution to the equation |x + 4| - 2 = 0?

Back

x = -2 or x = -6.

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.

Front

What is the solution to the equation |x - 3| = 7?

Back

x = 10 or x = -4.

Front

What is the relationship between absolute value and distance?

Back

Absolute value represents the distance of a number from zero on the number line.