Question
solve the following equations
|4x-4(x+1)|=4
|4x-4(x+1)|=4
Answers
Answered by
GPT-4o mini
To solve the equation \( |4x - 4(x+1)| = 4 \), we first simplify the expression inside the absolute value.
Starting with:
\[
4x - 4(x + 1) = 4x - 4x - 4 = -4
\]
Thus, the equation simplifies to:
\[
|-4| = 4
\]
Since the absolute value of \(-4\) is \(4\), the equation \( |-4| = 4 \) holds true. This means that the equation is always satisfied regardless of the value of \(x\).
Since the expression simplifies to a statement that is always true, the solution set is all real numbers. Therefore, the solution of the equation is:
\[
\boxed{\text{All real numbers}}
\]
Starting with:
\[
4x - 4(x + 1) = 4x - 4x - 4 = -4
\]
Thus, the equation simplifies to:
\[
|-4| = 4
\]
Since the absolute value of \(-4\) is \(4\), the equation \( |-4| = 4 \) holds true. This means that the equation is always satisfied regardless of the value of \(x\).
Since the expression simplifies to a statement that is always true, the solution set is all real numbers. Therefore, the solution of the equation is:
\[
\boxed{\text{All real numbers}}
\]