Solve the absolute value equation 4|7−x|+1=−1 .(1 point) Responses x=132 and x=152 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 x equals 7 x=152

Answer 1

Let's solve the absolute value equation step by step:

The equation is:

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

First, we can isolate the absolute value term by subtracting 1 from both sides:

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

This simplifies to:

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

Now, divide both sides by 4:

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

The absolute value of a number cannot be negative. Since \(|7 - x|\) represents a distance (which is always non-negative), this equation has no solution.

Thus, the answer is:

no solution.