Check for Balance: Are the Equations 9-x=1 and 5x=-40 Equal?

To determine if the two equations are balanced, we need to evaluate them separately:

First, we solve the equation $9 - x = 1$.

• Subtract 9 from both sides to isolate $-x$:
• $-x = 1 - 9$
• $-x = -8$
• Multiply both sides by $-1$ to solve for $x$:
• $x = 8$

Next, we solve the equation $5x = -40$.

• Divide both sides by 5 to isolate $x$:
• $x = \frac{-40}{5}$
• $x = -8$

The solution to the first equation is $x = 8$ and the solution to the second equation is $x = -8$. Since the solutions for $x$ are not the same, the two equations are not balanced.

Therefore, the correct answer is No.