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

Solve the equation |x - 5| = 3.

Back

x = 2 or x = 8.

Front

What does the equation |a| = b imply when b < 0?

Back

There is no solution, as absolute values cannot be negative.

Front

Solve |3x + 1| = 4.

Back

x = 1 or x = -rac{5}{3}.

Front

What is the solution to |x| = 0?

Back

x = 0.

Front

Solve |x + 2| + 3 = 7.

Back

x = 2 or x = -6.

Front

What is the general form of an absolute value equation?

Back

|expression| = constant.

Front

Solve |2x - 3| = 5.

Back

x = 4 or x = -1.

Front

What does |x - a| = b represent graphically?

Back

Two points on the number line, a distance b from a.

Front

Solve |x + 4| = 0.

Back

x = -4.