Question

mika used these steps to solve the equation ( 5x - 12 = -2 + 5(x - 2) ) which choice describes the meaning of her result, ( -12 = -12 )? step 1 ( 5x - 12 = -2 + 5(x - 2) ) step 2 ( 5x - 12 = -2 + 5x - 10 ) step 3 ( -5x ) ( -5x ) step 4 ( -12 = -2 - 10 ) step 5 ( -12 = -12 ) the result is not correct because the solution should be a positive integer no values of ( x ) make the equation true the solution is ( x = -12 ) all values of ( x ) make the equation true

Explanation:

When solving the equation \(5x - 12=-2 + 5(x - 2)\), after simplifying (distributing, combining like terms, and canceling \(5x\) from both sides), we get \(-12=-12\), which is a true statement. This means the equation is an identity, so all real values of \(x\) satisfy it. The other options are incorrect: the result is correct, \(x=-12\) is not the solution (since \(x\) canceled out), and it's not that no values work (it's the opposite).

Answer:

D. All values of \(x\) make the equation true (assuming the options are labeled with the last option as D, or matching the "All values of \(x\) make the equation true" option)