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Solve the equation for all values of $\mathrm{x}$.
\[
|4 x-8|+1=5 x
\]
Answer Attempt 1 out of 2
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\[
x=
\]
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Step 1 ：The given equation is \(|4x - 8| + 1 = 5x\). This is an absolute value equation, which means that the expression inside the absolute value can be either positive or negative. Therefore, we can split the equation into two cases.

Step 2 ：Case 1: \(4x - 8 + 1 = 5x\) when \(4x - 8 \geq 0\)

Step 3 ：Case 2: \(-(4x - 8) + 1 = 5x\) when \(4x - 8 < 0\)

Step 4 ：We can solve these two equations separately to find the possible values of x.

Step 5 ：Solving the first case, we find that there is no solution.

Step 6 ：Solving the second case, we find that the solution is x=1.

Step 7 ：However, we need to check if these solutions satisfy the original conditions. For the first case, there is no solution. For the second case, the solution x=1 does satisfy the condition \(4x - 8 < 0\).

Step 8 ：Therefore, the solution to the original equation is x=1.

Step 9 ：Final Answer: \(\boxed{1}\)