Question

Solve the following absolute value equation:

|x−3|=7


(1 point)
Responses

x=7, −7
x=7, −7

x=10, −4
x=10, −4

x=3, −7
x=3, −7

No solution

Answer 1

To solve the absolute value equation \( |x - 3| = 7 \), we need to consider the definition of absolute value, which implies two possible cases:

1. \( x - 3 = 7 \)
2. \( x - 3 = -7 \)

Let's solve each case:

1. **For the first case**:
\[
x - 3 = 7
\]
Adding 3 to both sides:
\[
x = 10
\]

2. **For the second case**:
\[
x - 3 = -7
\]
Adding 3 to both sides:
\[
x = -4
\]

Thus, the solutions are \( x = 10 \) and \( x = -4 \).

The correct response is:
**x=10, -4**