Question
Determine whether the equation below is an identity or whether it has no solution.
5(3xminus3)equals15(xminus3)
Question content area bottom
Part 1
Choose the correct answer below.
The equation is an identity.
The equation has no solution.
5(3xminus3)equals15(xminus3)
Question content area bottom
Part 1
Choose the correct answer below.
The equation is an identity.
The equation has no solution.
Answers
GPT-4o mini
To determine if the equation \(5(3x - 3) = 15(x - 3)\) is an identity or has no solution, let's simplify both sides.
Start with the left side:
\[
5(3x - 3) = 5 \cdot 3x - 5 \cdot 3 = 15x - 15
\]
Now simplify the right side:
\[
15(x - 3) = 15 \cdot x - 15 \cdot 3 = 15x - 45
\]
Now we have the simplified equation:
\[
15x - 15 = 15x - 45
\]
Next, we can try to isolate \(x\) by subtracting \(15x\) from both sides:
\[
-15 = -45
\]
This statement is not true (i.e., -15 does not equal -45), which indicates that there are no values of \(x\) that satisfy the original equation.
Thus, the equation has no solution.
The final answer is: **The equation has no solution.**
Start with the left side:
\[
5(3x - 3) = 5 \cdot 3x - 5 \cdot 3 = 15x - 15
\]
Now simplify the right side:
\[
15(x - 3) = 15 \cdot x - 15 \cdot 3 = 15x - 45
\]
Now we have the simplified equation:
\[
15x - 15 = 15x - 45
\]
Next, we can try to isolate \(x\) by subtracting \(15x\) from both sides:
\[
-15 = -45
\]
This statement is not true (i.e., -15 does not equal -45), which indicates that there are no values of \(x\) that satisfy the original equation.
Thus, the equation has no solution.
The final answer is: **The equation has no solution.**