Absolute Value Equations Review

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 |A| = B, you set up two equations: A = B and A = -B.

Front

What is the solution to the equation |x - 10| = 6?

Back

x = 16 or x = 4.

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 (e.g., |x| = -1 has no solution).

Front

Solve the equation |2a - 10| = 6. What are the solutions?

Back

a = 8 or a = 2.

Front

What are the two equations derived from |x + 6| = 4?

Back

x + 6 = 4 and x + 6 = -4.

Front

What is the solution to the equation -|−2r − 1| = 11?

Back

No Solution.

Front

How do you isolate the absolute value in an equation?

Back

To isolate the absolute value, you need to manipulate the equation so that the absolute value expression is alone on one side.

Front

What is the solution to the equation 8|-2x + 4| = 96?

Back

x = -4 or x = 8.

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.