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 )? 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:

Step1: Analyze the equation simplification

When solving an equation, if after simplification we get a statement like \(a = a\) (where \(a\) is a constant), it means that the equation is an identity.

Step2: Understand the nature of identity

An identity is true for all values of the variable. In the given equation \(5x−12 = −2 + 5(x−2)\), after expanding \(5(x - 2)=5x-10\) and subtracting \(5x\) from both sides, we get \(-12=-12\). This implies that no matter what value \(x\) takes, the left - hand side and the right - hand side of the original equation will always be equal.

Answer:

All values of \(x\) make the equation true.