Questions: Solve the equation and check your answer. -4(5-8x)-(1-x)=2(x-7) x= (Simplify your answer. Type an integer or a simplified fraction.)

Solve the equation and check your answer. -4(5-8x)-(1-x)=2(x-7) x= (Simplify your answer. Type an integer or a simplified fraction.)
Transcript text: Solve the equation and check your answer. \[ -4(5-8 x)-(1-x)=2(x-7) \] $x=$ $\square$ (Simplify your answer. Type an integer or a simplified fraction.)
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Solution

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Solution Steps

Step 1: Expand and Simplify the Equation

Start with the original equation: \[ -4(5-8x)-(1-x)=2(x-7) \] Expanding both sides gives: \[ -20 + 32x - 1 + x = 2x - 14 \] This simplifies to: \[ 33x - 21 = 2x - 14 \]

Step 2: Collect Like Terms

Rearranging the equation to isolate \(x\) involves moving all terms involving \(x\) to one side and constant terms to the other: \[ 33x - 2x = -14 + 21 \] This simplifies to: \[ 31x = 7 \]

Step 3: Solve for \(x\)

Dividing both sides by 31 gives: \[ x = \frac{7}{31} \]

Step 4: Verify the Solution

Substituting \(x = \frac{7}{31}\) back into the original equation confirms the solution: \[ -4(5 - 8 \cdot \frac{7}{31}) - (1 - \frac{7}{31}) = 2(\frac{7}{31} - 7) \] Both sides of the equation are equal, verifying that the solution is correct.

Final Answer

\(\boxed{x = \frac{7}{31}}\)

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