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 simplifying we get a statement like \(a = a\) (where \(a\) is a constant, here \(a=- 12\)), it means that the left - hand side and the right - hand side of the original equation are equivalent expressions for all values of the variable.

Let's start from the original equation \(5x−12=-2 + 5(x - 2)\).
Expand the right - hand side using the distributive property \(a(b + c)=ab+ac\). Here, \(5(x - 2)=5x-10\), so the equation becomes \(5x−12=-2 + 5x-10\).
Combine like terms on the right - hand side: \(-2-10=-12\), so we have \(5x−12=5x - 12\).
Subtract \(5x\) from both sides of the equation: \((5x−5x)-12=(5x−5x)-12\), which simplifies to \(-12=-12\).

Answer:

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