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 - 6| + 4 = 10?

Back

x = 12 and x = 0.

Front

What does the equation 8|-2x + 4| = 96 represent?

Back

It represents an absolute value equation that can be solved by isolating the absolute value expression and setting it equal to both positive and negative values.

Front

What are the solutions to the equation |8 - 4x| = 16?

Back

x = -2 and x = 6.

Front

What is the solution to the equation |4x - 3| = 17?

Back

x = 5 and x = -3.5.

Front

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

Back

It means that there are no values of the variable that can satisfy the equation, often because the absolute value cannot equal a negative number.

Front

What is the solution to the equation |−2n| + 10 = −50?

Back

No Solution.

Front

How do you graph an absolute value function?

Back

An absolute value function is graphed as 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 on the number line.