Expressions and Equations: Identifying Equivalent Expressions (CCSS.6.EE.4)

Distribute 2: $2(x+3)=2\cdot x+2\cdot 3=2x+6$. A ($2x+3$) only distributes to $x$. C ($x+3$) ignores the 2. D ($2x-6$) has the wrong sign on the constant.

Simplify the original: $5z-2z+4=(5-2)z+4=3z+4$. A and B both equal $3z+4$. C equals $3z+4$ because $z+z+z=3z$. D is $3(z+4)=3z+12$, which is not equal to $3z+4$.

Distribute the minus sign: $4y-(2y-5)=4y-2y+5=2y+5$. B forgets to change the sign on 5. C incorrectly adds $4y$ and $2y$ and also misses the $+5$. D equals $2y+10$, not $2y+5$.

Simplify the original: $3(x-4)+x=3x-12+x=4x-12$. A is already $4x-12$. B simplifies to $4x-12$. D equals $4x-12$ because $2(2x-6)=4x-12$. C has $4x+12$, the wrong sign on the constant.

Distribute 2 to both terms: $2(x+3)=2\cdot x+2\cdot 3=2x+6$. Choice B distributes only to $x$. Choice C drops the factor on $x$. Choice D incorrectly changes the sign of the constant.

Combine like terms: $4y-2y=2y$, so the expression simplifies to $2y+5$. Choices A and C both equal $2y+5$ (order doesn't matter). Choice B is $y+y+5=2y+5$. Choice D is $3y+5$, which is not equal to $2y+5$.

Distribute $-3$ to both terms: $-3(2a-4)=(-3)\cdot 2a+(-3)\cdot(-4)=-6a+12$. Choice A makes the second term negative. Choice C fails to distribute. Choice D loses the negative factor.

Combine like terms: $7n-3n=4n$, so the expression becomes $4n+9$. Choice A adds $7n$ and $3n$ instead of subtracting. Choice B changes the sign of the constant. Choice D subtracts the constant incorrectly.

Distribute $2$ to both terms: $2(x+3)=2\cdot x+2\cdot 3=2x+6$. Choice A ($2x+3$) only distributes to $x$. Choice C ($x+6$) misses a factor of $2$ on $x$. Choice D ($x+3x+3=4x+3$) adds unlike terms incorrectly.

Simplify: $3(y-4)+2y=3y-12+2y=5y-12$. Choices A, B, and C all represent $5y-12$ in different orders/forms. Choice D ($5y+12$) has the wrong sign on the constant.