Adam solved the equation $$ 12x+15+3x−5 = 9x+20+3x−5 $$ in the following way:
(1) He added $(−3x)$, and then he added $5$ to both sides of the equation: $$ 12x−3x+15+5+3x−5=9x+20 $$
(2) He reorganized the terms on the left side of the equation to separate the binomial $9x+20$: $$ (9x+20)+(3x−5)=9x+20 $$
(3) He subtracted $(9x+20)$ from both sides of the equation and obtained: $$ (9x+20)−(9x+20) + (3x−5)−(9x+20) =9x+20−(9x+20) $$
(4) By removing the parentheses and simplifying both sides of the equation, he got: $$ 3x − 5 − 9x − 20 = 0 $$
(5) He combined the ’$x$’ terms on the left side and brought the constant terms to the right side: $$ −6x = 25 $$
(6) Finally, he got the solution: $$ x = −\frac{25}6 $$ In which step and what did Adam do wrong? Give explanation.
In step (3). He subtracted the expression $9x+20$ twice on the left side of the equation.
In step (4). The right side of the equation must yield $40$.
In step (1). By adding $(−3x+5)$ to both sides of the equation, he should obtain $9x+20=6x+25$.
In step (6). By moving $−6$ to the other side of the equation, he should obtain $x=31$.
$$ \begin{alignat}2 12x+15+3x-5&=9x+20+3x-5 \quad&&\big/-(3x-5) \cr 12x+15&=9x+20 &&\big/ +(-9x-15) \cr 3x&=5 &&\big/ \cdot \frac13 \cr x&=\frac35 \end{alignat} $$