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

To solve the given equation $7(x + 5) - 3(x - 2) = 5$, we follow these steps:

• Step 1: Apply the distributive property.
  Distribute 7 over $(x + 5)$ to obtain $7x + 35$.
  Distribute -3 over $(x - 2)$ to obtain $-3x + 6$.
  The equation becomes $7x + 35 - 3x + 6 = 5$.
  
• Step 2: Combine like terms.
  Combine the $x$ terms $7x$ and $-3x$ to get $4x$.
  Combine the constant terms $35$ and $6$ to get $41$.
  The equation simplifies to $4x + 41 = 5$.
  
• Step 3: Isolate the variable $x$.
  Subtract 41 from both sides: $4x + 41 - 41 = 5 - 41$.
  This simplifies to $4x = -36$.
  Divide both sides by 4 to solve for $x$: $x = \frac{-36}{4}$.
  The solution is $x = -9$.

Therefore, the solution to the equation is $x = -9$.