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

What does the equation |x + 9| = -5 imply?

Back

This equation has no solution because absolute values cannot be negative.

Front

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

Back

Set up two equations: 2a - 10 = 6 and 2a - 10 = -6. Solve to find a = 8 and a = 2.

Front

What is the solution set for |v + 8| - 5 = 2?

Back

The solution set is {-1, -15}.

Front

How do you solve |2x + 9| = 15?

Back

Set up two equations: 2x + 9 = 15 and 2x + 9 = -15. Solve to find x = 3 and x = -12.

Front

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

Back

Subtract 4 from both sides to get |x - 6| = 6.

Front

What are the possible solutions for |x - 6| = 6?

Back

The solutions are x = 12 and x = 0.

Front

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

Back

It means that there are no values for the variable that can satisfy the equation.

Front

How can you express |x| = a in terms of two equations?

Back

You can express it as x = a and x = -a, where a is a non-negative number.

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.