Question

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

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

x=7
x equals 7

no solution
no solution

x=132
and x=152

Answer 1

To solve the equation \( 4|7 - x| + 1 = -1 \), we start by isolating the absolute value:

\[
4|7 - x| + 1 = -1
\]

Subtract 1 from both sides:

\[
4|7 - x| = -2
\]

Now, divide both sides by 4:

\[
|7 - x| = -\frac{1}{2}
\]

Since the absolute value cannot be negative, \( |7 - x| = -\frac{1}{2} \) has no solutions.

Therefore, the answer is:

**no solution**.