Question

find the error a student solved the equation and determined that the solution was -2. choose the response that shows her error and corrects it.
15x - 2 = -2 + 15x
-2 = -2
a) there is no error, her answer is correct.
b) the initial equation simplifies to 3x = 0, which means that x = 0.
c) the equation -2 = -2 is always true, so no value of x will make the equation true. the correct solution of the equation is that there is no solution.
d) the equation -2 = -2 is always true, so every value of x will make the equation true. the correct solution of the equation is infinitely many solution

Explanation:

1. First, analyze the given equation \(1.5x - 2=-2 + 1.5x\).

• Subtract \(1.5x\) from both sides: \((1.5x-1.5x)-2=(-2)+(1.5x - 1.5x)\).
• This simplifies to \(-2=-2\).
• The equation \(-2 = -2\) is an identity, which means it is true for all real - valued \(x\). So the student's conclusion that the solution is \(-2\) is wrong.
• Option A is wrong because the student's answer (\(x = - 2\)) is incorrect.
• Option B is wrong because when we simplify \(1.5x-2=-2 + 1.5x\), we get \(-2=-2\) (not \(3x = 0\)).
• Option C is wrong because \(-2=-2\) is always true, which means the equation has infinitely many solutions (all real numbers \(x\)) not no solution.
• Option D correctly states that since \(-2=-2\) is always true, every value of \(x\) will satisfy the equation, so the equation has infinitely many solutions.

Answer:

D) The equation \(-2=-2\) is always true, so every value of \(x\) will make the equation true. The correct solution of the equation is infinitely many solutions.