Question

elena said the equation $9x + 15 = 3x + 15$ has no solutions because $9x$ is greater than $3x$. select the correct choice from the drop down. do you agree with elena?

Explanation:

Step1: Solve the equation \(9x + 15 = 3x + 15\)

Subtract \(3x\) from both sides: \(9x - 3x + 15 = 3x - 3x + 15\)
Simplify: \(6x + 15 = 15\)

Step2: Isolate the variable term

Subtract 15 from both sides: \(6x + 15 - 15 = 15 - 15\)
Simplify: \(6x = 0\)

Step3: Solve for \(x\)

Divide both sides by 6: \(\frac{6x}{6} = \frac{0}{6}\)
Simplify: \(x = 0\)
Since we found a solution (\(x = 0\)) for the equation, Elena's reasoning is incorrect because the equation does have a solution.

Answer:

No, I do not agree with Elena. The equation \(9x + 15 = 3x + 15\) can be solved as follows: subtract \(3x\) from both sides to get \(6x + 15 = 15\), then subtract 15 from both sides to get \(6x = 0\), and finally divide by 6 to find \(x = 0\), so the equation has a solution (\(x = 0\)).