7. Which equation has the same first step to solve as this equation: 2x+12−3x=27 (1 point) Responses 2x+12=−3x−27 2 x plus 12 is equal to negative 3 x minus 27 4x−17+2x=9 4 x minus 17 plus 2 x is equal to 9 2(x−5)+2x=10 2 times open paren x minus 5 close paren plus 2 x is equal to 10 2x+12=27

Question

GPT-4o mini · Answer

To solve the equation $2x + 12 - 3x = 27$, the first step typically involves isolating the variable $x$ by combining like terms. In this case, we first combine $2x$ and $-3x$: $$ 2x - 3x + 12 = 27 \implies -x + 12 = 27 $$ Now, we can look at the provided responses for an equation that requires the same first step of combining like terms. 1. $2x + 12 = -3x - 27$ - This does not apply as it is already an equation without like terms on the left side. 2. $4x - 17 + 2x = 9$ - Here, we combine $4x$ and $2x$ as the first step. 3. $2(x - 5) + 2x = 10$ - This requires distribution first and doesn’t match our step. 4. $2x + 12 = 27$ - This further isolates $x$ directly, not a like terms equation. The second option, **$4x - 17 + 2x = 9$**, has the same first step by combining like terms (specifically, combining $4x$ and $2x$) as in the original equation. Thus, the answer is: **4x - 17 + 2x = 9**