Solve for X: -7(x+4)-2=5(2-x) Linear Equation Solution

To solve the equation $-7(x+4)-2=5(2-x)$, follow these steps:

• Step 1: Distribute the coefficients across the terms inside the parentheses.
  On the left side: Apply $-7$ to $(x + 4)$:
  $-7 \cdot x + (-7) \cdot 4 = -7x - 28$.
  On the right side: Apply $5$ to $(2 - x)$:
  $5 \cdot 2 + 5 \cdot (-x) = 10 - 5x$.
• Step 2: Substitute the distributed expressions back into the equation:
  $-7x - 28 - 2 = 10 - 5x$.
• Step 3: Simplify both sides by combining like terms:
  The left side simplifies to: $-7x - 30$.
  Thus, the equation becomes: $-7x - 30 = 10 - 5x$.
• Step 4: Get all terms involving $x$ on one side of the equation:
  Add $5x$ to both sides: $-7x + 5x - 30 = 10$.
  This simplifies to: $-2x - 30 = 10$.
• Step 5: Isolate the term with $x$ on one side:
  Add $30$ to both sides: $-2x = 40$.
• Step 6: Solve for $x$ by dividing by $-2$:
  $x = \frac{40}{-2} = -20$.

Therefore, the solution to the equation is $x = -20$.