Solving Absolute Value Equations

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 |A| = B, you set up two equations: A = B and A = -B, then solve for the variable.

Front

Solve for a: |2a - 10| = 6

Back

a = 8, a = 2

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 a negative number.

Front

Solve for x: |3x - 6| - 9 = -3

Back

x = 0 and x = 4

Front

What is the solution set for the equation 0 = -6|9v - 7|?

Back

one solution

Front

Solve for p: 9|9 - 2p| = 81

Back

p = 0, p = 9

Front

What is the significance of the negative sign in front of an absolute value?

Back

A negative sign in front of an absolute value indicates that the expression is being multiplied by a negative number, which can affect the solution.

Front

Solve for r: −2|−2r − 4| = -12

Back

{-3, -1}

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.