Asked by Honeybeee
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
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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**.
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**.
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