Questions: Solve the equation for (x). [ 6 x-1+3=17 ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (square) . (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate B. The solution set is (varnothing).

Solution Steps

To solve the equation \(|6x - 1| + 3 = 17\), we first isolate the absolute value expression and then consider the two possible cases for the expression inside the absolute value.

1. Isolate the absolute value: \(|6x - 1| = 14\).
2. Consider the two cases:
   • Case 1: \(6x - 1 = 14\)
   • Case 2: \(6x - 1 = -14\)
3. Solve each case for \(x\).

Given the equation: \[ |6x - 1| + 3 = 17 \] First, isolate the absolute value expression by subtracting 3 from both sides: \[ |6x - 1| = 14 \]

The absolute value equation \(|6x - 1| = 14\) can be split into two cases:

1. \(6x - 1 = 14\)
2. \(6x - 1 = -14\)

\[ 6x - 1 = 14 \] Add 1 to both sides: \[ 6x = 15 \] Divide by 6: \[ x = \frac{15}{6} = \frac{5}{2} \]

\[ 6x - 1 = -14 \] Add 1 to both sides: \[ 6x = -13 \] Divide by 6: \[ x = \frac{-13}{6} \]

Final Answer