Question

Which equation is equivalent to

−4(3x + 2) = x + 2(x − 1)?

A. −12x + 2 = 3x − 1
B. −12x − 8 = 2x − 2
C. −8 = 15x − 2
D. −15x = −10

Answer 1

Let's start by simplifying both sides of the equation:

−4(3x + 2) = x + 2(x − 1)

−12x − 8 = x + 2x − 2 (distributing the negative 4)

−12x − 8 = 3x - 2 (combining like terms)

Now we can add 12x to both sides and add 2 to both sides:

−12x − 8 + 12x + 2 = 3x - 2 + 12x + 2

−6x = 0

Finally, we can divide both sides by -6 to isolate x:

x = 0

Now we can check which of the given equations is equivalent to this solution:

A. −12x + 2 = 3x − 1 (substituting x = 0 gives 2 = -1, which is false)

B. −12x − 8 = 2x − 2 (substituting x = 0 gives -8 = -2, which is false)

C. −8 = 15x − 2 (substituting x = 0 gives -8 = -2, which is false)

D. −15x = −10 (substituting x = 0 gives 0 = 0, which is true)

So the answer is D.

Answer 2

• C. -8 = 15x - 2

Explanation:

First, let's solve the equation -4(3x + 2) = x + 2(x − 1):-

• 
  `\mathrm{-4\left(3x+2\right)=x+2\left(x-1\right)}`
• 
  `\mathrm{-12x-8=x+2x-2}`
• 
  `\mathrm{-12x-8=3x-2}`
• 
  `\mathrm{-12x-8=3x-2}`
• 
  `\mathrm{-15x=6}`

• 
  `\mathrm{(-15x)/(-15)=(6)/(-15)}`

→
`\boxed{\bf {x=-(2)/(5)\;\;or\:\:x=-0.4}}`

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A. -12x + 2 = 3x - 1

• -12(-2/5) + 2 = 3(-2/5) - 1
• 34/5=-11/5

The sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).

________________________

B. -12x - 8 = 2x - 2

• -12(-2/5) - 8 = 2(-2/5) - 2
• -16/5=-14/5

Sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).

________________________

C. −8 = 15x − 2

• -8 = 15(-2/5) - 2
• -8=-8

Sides are equal therefore, this equation is True and is equivalent to −4(3x + 2) = x + 2(x − 1).

________________________

D. -15x = -10

• -15(-2/5) = -10
• 6 = -10

Sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).

Hence, C. -8 = 15x - 2 is the only equation equivalent to -4(3x + 2) = x + 2(x - 1).

______________________

Hope this helps!