Question

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

Explanation:

Step1: Isolate the absolute - value term

First, subtract 10 from both sides of the equation $-|10 + x|+10=-1$.
$-|10 + x|=-1 - 10$
$-|10 + x|=-11$
Then multiply both sides by - 1 to get $|10 + x| = 11$.

Step2: Consider two cases

Case 1: When $10 + x\geq0$ (i.e., $x\geq - 10$), the absolute - value equation $|10 + x| = 11$ becomes $10 + x = 11$.
Subtract 10 from both sides: $x=11 - 10=1$.
Case 2: When $10 + x\lt0$ (i.e., $x\lt - 10$), the absolute - value equation $|10 + x| = 11$ becomes $-(10 + x)=11$.
Expand the left - hand side: $-10 - x = 11$.
Add 10 to both sides: $-x=11 + 10$, so $-x = 21$.
Multiply both sides by - 1: $x=-21$.

Answer:

$x = 1$ or $x=-21$