Question

what equation has the same solution as x - 12 = 40

Answer 1

To find an equation that has the same solution as \(x - 12 = 40\), we first solve the original equation for \(x\):

1. \(x - 12 = 40\)
2. Add 12 to both sides:
\[
x = 40 + 12
\]
3. Simplifying gives us:
\[
x = 52
\]

Now, we can create a new equation that also has the solution \(x = 52\). For example, we can simply add or subtract the same number from both sides of the original equation. One possible equation could be:

\[
x - 12 - 5 = 40 - 5
\]

Simplifying this, we have:

\[
x - 17 = 35
\]

Thus, the equation \(x - 17 = 35\) has the same solution as \(x - 12 = 40\) since both yield \(x = 52\). There are infinitely many equations you can create that will have the same solution; another example could be:

\[
x - 12 + 10 = 40 + 10
\]

This simplifies to:

\[
x - 2 = 50
\]

This, too, has the same solution \(x = 52\).