Question

charlie used these steps to solve the equation (6x + 5 = 1+2(3x + 2)). which choice describes the meaning of his result, (5 = 5)?
step 1 (6x + 5 = 1+2(3x + 2))
step 2 (6x + 5 = 1+6x + 4)
step 3 (\frac{-6x}{}\frac{-6x}{})
step 4 (5 = 1+4)
step 5 (5 = 5)
all values of (x) make the equation true.
the solution is (x = 5).
no values of (x) make the equation true.
the result is not correct because step 2 has an error.

Explanation:

Step1: Analyze the equation simplification

The original equation is \(6x + 5=1 + 2(3x + 2)\).
After expanding \(2(3x + 2)\) to \(6x+4\) (Step 2: \(6x + 5=1 + 6x + 4\)), and then subtracting \(6x\) from both sides (Step 3), we get \(5 = 5\).
This means 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.