Verify: Are the Equations x-25=5 and 7x-10=200 Balanced?

Are the equations balanced?

$x-25=5\stackrel{?}{=}7x-10=200$

We will solve each equation step-by-step to ascertain if there is a common solution indicative of them being balanced:

Solving the first equation $x - 25 = 5$:

• Add 25 to both sides to isolate $x$:

Solving the second equation $7x - 10 = 200$:

• Add 10 to both sides to isolate the term with $x$:

• Divide by 7 to solve for $x$:

Both equations give the solution $x = 30$. This indicates that they are indeed balanced, as they share a common solution for $x$.

Therefore, the equations are balanced.

The correct answer to the problem is: Yes.