Solve \( 1-\frac{1}{7} x-31+8=3 \) Enter your answer as a reduced fraction (like 5/3, not 10/6) or as an integer (like 4 or -2 ). Do not enter mixed numbers. Enter DNE for Does Not Exist, oo for Infinity The solutions (where \( x_{1} \leq x_{2} \) ) are \( x_{1}= \) \( x_{2}= \)
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First, let's simplify the equation step by step: Starting with the equation: \[ 1 - \frac{1}{7} x - 31 + 8 = 3 \] Combine the constant terms: \[ 1 - 31 + 8 = -22 \] So the equation becomes: \[ -\frac{1}{7} x - 22 = 3 \] Now, let's isolate the term with \( x \): \[ -\frac{1}{7} x = 3 + 22 \] \[ -\frac{1}{7} x = 25 \] Next, multiply both sides by -7 to solve for \( x \): \[ x = -7 \cdot 25 \] \[ x = -175 \] Since the problem doesn't specify a second solution, we conclude: \( x_{1} = -175 \) and there are no other solutions. Thus, the final answers are: \( x_{1} = -175 \) \( x_{2} = DNE \)