Solve for X: -7/4(-x) + 2x - 5(x+3) = -x Linear Equation

$-\frac{7}{4}(-x)+2x-5(x+3)=-x$

$x=\text{?}$

To solve the given linear equation $-\frac{7}{4}(-x) + 2x - 5(x + 3) = -x$, follow these steps:

• Step 1: Distribute the coefficients across the terms within parentheses:
  The term $-\frac{7}{4}(-x)$ becomes $\frac{7}{4}x$ because $-\frac{7}{4} \times -x = \frac{7}{4}x$.
  The term $-5(x + 3)$ can be expanded to $-5x - 15$.
• Step 2: Simplify the equation by combining like terms:
  The equation becomes $\frac{7}{4}x + 2x - 5x - 15 = -x$.
• Step 3: Combine the $x$-terms on the left side:
  Combine: $\frac{7}{4}x + 2x - 5x$.
  Converting all terms to a common denominator, $2x = \frac{8}{4}x$ and $-5x = \frac{-20}{4}x$. Thus,
  $\frac{7}{4}x + \frac{8}{4}x - \frac{20}{4}x = \frac{-5}{4}x$.
• Step 4: The equation simplifies to:
  $\frac{-5}{4}x - 15 = -x$.
• Step 5: Isolate the $x$ terms onto one side:
  Add $x$ to both sides, treating $-x$ as $\frac{-4}{4}x$:
  $\frac{-5}{4}x + x - 15 = 0$, which simplifies to $\frac{-1}{4}x - 15 = 0$.
• Step 6: Isolate $x$:
  Add $15$ to both sides:
  $\frac{-1}{4}x = 15$.
• Step 7: Solve for $x$:
  Multiply both sides by $-4$ to isolate $x$:
  $x = 15 \times -4$.
  Thus, $x = -60$.

Therefore, the solution to the equation is $x = -60$.