Question

which expressions are equivalent to 5x - 8x + 12y? (choose 3) a 3(x - 4y) b 3(-x + 4y) c -3x + 12y d -3(x - 4y) e -3(-x + 4y)

Explanation:

Step1: Simplify the original expression

First, combine like terms in \(5x - 8x + 12y\). The like terms for \(x\) are \(5x\) and \(-8x\). So, \(5x-8x=(5 - 8)x=-3x\). Thus, the original expression simplifies to \(-3x + 12y\).

Step2: Analyze Option A

Expand \(3(x - 4y)\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a = 3\), \(b=x\), \(c=-4y\). So, \(3(x - 4y)=3x-12y\), which is not equivalent to \(-3x + 12y\).

Step3: Analyze Option B

Expand \(3(-x + 4y)\) using the distributive property. \(3(-x)+3(4y)=-3x + 12y\), which matches the simplified original expression.

Step4: Analyze Option C

Option C is \(-3x + 12y\), which is exactly the simplified form of the original expression, so it is equivalent.

Step5: Analyze Option D

Expand \(-3(x - 4y)\) using the distributive property. \(-3(x)+(-3)(-4y)=-3x + 12y\), which is equivalent to the simplified original expression.

Step6: Analyze Option E

Expand \(-3(-x + 4y)\) using the distributive property. \(-3(-x)+(-3)(4y)=3x-12y\), which is not equivalent to \(-3x + 12y\).

Answer:

B. \(3(-x + 4y)\), C. \(-3x + 12y\), D. \(-3(x - 4y)\)