Question

Determine whether the equation below is an identity or whether it has no solution.
5​(5xminus15​)equals25​(xminus15​)
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Part 1
Choose the correct answer below.
The equation is an identity.
The equation has no solution.

Answer 1

To determine whether the equation \( 5(5x - 15) = 25(x - 15) \) is an identity or has no solution, let's simplify both sides of the equation.

Starting with the left side:
\[
5(5x - 15) = 25x - 75
\]

Now, simplifying the right side:
\[
25(x - 15) = 25x - 375
\]

Now we can rewrite the equation:
\[
25x - 75 = 25x - 375
\]

Next, we can subtract \( 25x \) from both sides:
\[
-75 = -375
\]

This statement is false, as \(-75\) does not equal \(-375\).

Since we derived a false statement, this means the original equation has no solution.

**The answer is: The equation has no solution.**