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4(−x+2)−4x+2=

−38

1 answer

To solve the equation \( 4(-x+2) - 4x + 2 = -38 \), let's first simplify the left-hand side.

  1. Distribute the 4 in the term \( 4(-x + 2) \): \[ 4(-x) + 4(2) = -4x + 8 \]

  2. Substitute this back into the equation: \[ -4x + 8 - 4x + 2 = -38 \]

  3. Combine like terms: \[ -4x - 4x + 8 + 2 = -38 \] \[ -8x + 10 = -38 \]

  4. Next, isolate the term with \( x \) by subtracting 10 from both sides: \[ -8x = -38 - 10 \] \[ -8x = -48 \]

  5. Now, divide both sides by -8 to solve for \( x \): \[ x = \frac{-48}{-8} \] \[ x = 6 \]

The solution is \( x = 6 \).