Question

Solve the absolute value equation 4|7−x|+1=−1
4
|
7
−
𝑥
|
+
1
=
−
1
.(1 point)
Responses

x=152
𝑥
=
15
2
x equals Start Fraction 15 over 2 End Fraction

x=132
𝑥
=
13
2
and x=152
𝑥
=
15
2
x equals Start Fraction 13 over 2 End Fraction and x equals Start Fraction 15 over 2 End Fraction

no solution
no solution

x=7

Answer 1

To solve the equation \( 4|7 - x| + 1 = -1 \), we first isolate the absolute value expression.

1. Subtract 1 from both sides:
\[
4|7 - x| + 1 - 1 = -1 - 1 \\
4|7 - x| = -2
\]

2. Divide both sides by 4:
\[
|7 - x| = -\frac{1}{2}
\]

The absolute value of any expression cannot be negative. Since \( |7 - x| \) is defined to be non-negative (it represents a distance), this means that the equation \( |7 - x| = -\frac{1}{2} \) has no solution.

Thus, the final answer is:

**no solution**