Question

question
solve for all values of x in simplest form.
-|10 + x| + 10 = -1

Explanation:

Step1: Isolate the absolute value term

Subtract 10 from both sides:
$$-|10+x| = -1 - 10$$
$$-|10+x| = -11$$
Multiply both sides by -1:
$$|10+x| = 11$$

Step2: Split into two cases

Case 1: Inside absolute value is non-negative
$$10+x = 11$$
Case 2: Inside absolute value is negative
$$10+x = -11$$

Step3: Solve Case 1

Subtract 10 from both sides:
$$x = 11 - 10$$
$$x = 1$$

Step4: Solve Case 2

Subtract 10 from both sides:
$$x = -11 - 10$$
$$x = -21$$

Answer:

$x = 1$ and $x = -21$