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 of the form |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What is the solution set for the equation |x| = 9?

Back

The solution set is {9, -9}.

Front

How do you solve an equation of the form |ax + b| = c?

Back

You isolate the absolute value expression and then set up two cases: ax + b = c and ax + b = -c.

Front

What is the solution to the equation |5x| = 40?

Back

The solutions are x = 8 and x = -8.

Front

How do you interpret the equation |2a - 10| = 6?

Back

This equation means that the expression 2a - 10 is either equal to 6 or -6.

Front

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

Back

The solutions are a = 8 and a = 2.

Front

What is the first step in solving the equation |x - 6| + 4 = 10?

Back

First, isolate the absolute value by subtracting 4 from both sides: |x - 6| = 6.

Front

What are the solutions to the equation |x - 6| = 6?

Back

The solutions are x = 12 and x = 0.

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.