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, set up two equations: x = a and x = -a.

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| = -5 has no solution).

Front

Solve the equation |x - 5| = 3.

Back

x = 8 or x = 2.

Front

What is the first step in solving the equation |2x + 4| = 10?

Back

Set up two equations: 2x + 4 = 10 and 2x + 4 = -10.

Front

Solve the equation |x + 3| - 2 = 5.

Back

x = 4 or x = -8.

Front

What is the solution set for the equation |x| = 0?

Back

The solution set is {0}.

Front

How do you interpret the equation |x - 12| - 3 = 11?

Back

This means that the distance between x and 12, minus 3, equals 11.

Front

Solve the equation |3x - 6| = 12.

Back

x = 6 or x = -2.

Front

What is the solution to the equation |x| + 5 = 0?

Back

No Solution, since |x| cannot be negative.