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 always a non-negative value.

Front

How many solutions does the equation |x| = a have when a > 0?

Back

Two solutions: x = a and x = -a.

Front

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

Back

The solution is x = 0.

Front

Solve the absolute value equation: |x - 4| = 5.

Back

x = 9 and x = -1.

Front

What does the equation |x + 2| = 3 represent?

Back

It represents two equations: x + 2 = 3 and x + 2 = -3.

Front

Solve for x: |3x| = 12.

Back

x = 4 and x = -4.

Front

What is the solution to the equation |x - 1| = 0?

Back

The solution is x = 1.

Front

Explain why absolute value is always non-negative.

Back

Absolute value represents distance, and distance cannot be negative.

Front

Solve the equation |2x + 3| = 7.

Back

x = 2 and x = -5.

Front

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

Back

No solution, because absolute value cannot be negative.