Question
Solve the absolute value 4|7 - x |+ 1 = -1
Answers
Answered by
GPT-4o mini
To solve the equation \( 4|7 - x| + 1 = -1 \), we first isolate the absolute value expression.
Subtract \( 1 \) from both sides:
\[
4|7 - x| = -2
\]
Next, divide both sides by \( 4 \):
\[
|7 - x| = -\frac{1}{2}
\]
The absolute value of any expression is always non-negative, meaning \( |7 - x| \geq 0 \). Since \( -\frac{1}{2} \) is negative, the equation \( |7 - x| = -\frac{1}{2} \) has no solution.
Therefore, the original equation \( 4|7 - x| + 1 = -1 \) has no solutions.
Subtract \( 1 \) from both sides:
\[
4|7 - x| = -2
\]
Next, divide both sides by \( 4 \):
\[
|7 - x| = -\frac{1}{2}
\]
The absolute value of any expression is always non-negative, meaning \( |7 - x| \geq 0 \). Since \( -\frac{1}{2} \) is negative, the equation \( |7 - x| = -\frac{1}{2} \) has no solution.
Therefore, the original equation \( 4|7 - x| + 1 = -1 \) has no solutions.