$$ |x-2|=9 $$ $$ x=\square $$ (smaller value) $$ x=\square $$ (larger value)

Question

UpStudy AI · Accepted Answer

To solve the equation $$ |x - 2| = 9 $$, we consider the definition of absolute value, which leads to two possible scenarios:

1. **Positive Case:**
   $$
   x - 2 = 9 \
   x = 9 + 2 \
   x = 11
   $$

2. **Negative Case:**
   $$
   x - 2 = -9 \
   x = -9 + 2 \
   x = -7
   $$

Therefore, the solutions are:

$$
x = -7 \quad \text{(smaller value)}
$$
$$
x = 11 \quad \text{(larger value)}
$$
$$ x = -7 $$ and $$ x = 11 $$.

(smaller value)
(larger value)