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 the equation |x - a| = b?

Back

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

Front

What is the solution to the equation |x - 3| = 0?

Back

The solution is x = 3, since the absolute value is zero only when the expression inside is zero.

Front

Can the absolute value of a number be negative?

Back

No, the absolute value of a number is always non-negative.

Front

What does the equation |x + 5| = -3 imply?

Back

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

Front

Solve for x: |x - 6| + 4 = 10.

Back

x = 12 and x = 0.

Front

Solve for a: |2a - 10| = 6.

Back

a = 8 and a = 2.

Front

What is the solution to the equation |2x - 3| + 5 = 10?

Back

The solutions are x = -1 and x = 4.

Front

If |x + 9| = -5, what can be concluded?

Back

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

Front

What is the first step in solving |x - 4| = 3?

Back

Set up two equations: x - 4 = 3 and x - 4 = -3.