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

Solve for x: |5x| = 40

Back

x = 8 and x = -8

Front

Solve for x: |3x + 2| = 5

Back

x = -2.333... and x = 1

Front

Solve for x: |x - 6| + 4 = 10

Back

x = 12 and x = 0

Front

Solve for x: |8 - 4x| = 16

Back

x = -2 and x = 6

Front

Solve for x: |4x - 3| = 17

Back

x = 5 and x = -3.5

Front

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

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal the given value on the other side of the equation.

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 represents the distance of a number from zero, which is always a non-negative value.