Question

question 6 · 1 point

solve: \\(-|w - 10| + 2 = 8\\).
(use a comma to separate multiple solutions. enter in fraction form or

provide your answer below:

\\(w =\\)

Explanation:

Isolate the absolute value term

To solve the equation, we first isolate the absolute value expression on one side.

$$ -|w - 10| + 2 = 8 $$

Subtract \(2\) from both sides:

$$ -|w - 10| = 6 $$

Multiply by negative one

Multiply both sides of the equation by \(-1\) to fully isolate the absolute value expression.

$$ |w - 10| = -6 $$

Analyze the isolated equation

We examine the properties of absolute value. The absolute value of any real number represents its distance from zero on the number line. Since distance cannot be negative, the absolute value of any expression must be greater than or equal to zero:

$$ |w - 10| \ge 0 $$

However, our equation states:

$$ |w - 10| = -6 $$

Since a non-negative quantity can never equal a negative number, this equation has no solution.

Answer:

Solve: \(-|w - 10| + 2 = 8\).

\(w =\) <blank>No solution</blank>