Questions: 12-8x-1=6

12-8x-1=6
Transcript text: Do Homework - HW 6 https://mylab.pearson.com/Student/PlayerHomework.aspx? F Fall 2024 N 6 Solve. \[ 12-|8 x-1|=6 \]
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Solution

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Solution Steps

To solve the equation \(12 - |8x - 1| = 6\), we first isolate the absolute value expression. Then, we consider the two cases for the absolute value: one where the expression inside is positive and one where it is negative. Solve each resulting equation separately to find the possible values of \(x\).

Step 1: Isolate the Absolute Value Expression

The given equation is:

\[ 12 - |8x - 1| = 6 \]

First, we need to isolate the absolute value expression. Subtract 12 from both sides:

\[ -|8x - 1| = 6 - 12 \]

Simplify the right side:

\[ -|8x - 1| = -6 \]

Multiply both sides by -1 to remove the negative sign:

\[ |8x - 1| = 6 \]

Step 2: Solve the Absolute Value Equation

The equation \(|8x - 1| = 6\) implies two separate equations:

  1. \(8x - 1 = 6\)
  2. \(8x - 1 = -6\)
Case 1: \(8x - 1 = 6\)

Add 1 to both sides:

\[ 8x = 6 + 1 \]

\[ 8x = 7 \]

Divide both sides by 8:

\[ x = \frac{7}{8} \]

Case 2: \(8x - 1 = -6\)

Add 1 to both sides:

\[ 8x = -6 + 1 \]

\[ 8x = -5 \]

Divide both sides by 8:

\[ x = -\frac{5}{8} \]

Final Answer

The solutions to the equation are:

\[ \boxed{x = \frac{7}{8}} \]

\[ \boxed{x = -\frac{5}{8}} \]

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