Question

1) 4(x-1)=2(2x-8)+12 2) 7(4x-1)=6-2(3-14x)

Answer 1

4(x-1)=2(2x-8)+12

4х-4=4х-16+12

-4=-16+12

-4=-4

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7(4x-1)=6-2(3-14x)

28х-7=6-6+28х

-7=6-6

-7=0

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Answer 2

4(x-1)=2(2x-8)+12

4х-4=4х-16+12

-4=-16+12

решений нет

7(4x-1)=6-2(3-14x)

28х-7=6-6+28х

-7=6-6

решений нет

Answer 3

To solve the given equations, we'll start by simplifying both sides of the equations and then isolating the variable $x$. Let's solve each equation step by step:

1) $4(x-1) = 2(2x-8) + 12$

Expand both sides:

$4x - 4 = 4x - 16 + 12$

Combine like terms:

$4x - 4 = 4x - 4$

Now, you can see that both sides of the equation are the same. This means that the equation has infinitely many solutions. Any value of $x$ will satisfy the equation.

2) $7(4x-1) = 6 - 2(3-14x)$

Expand both sides:

$28x - 7 = 6 - 6 + 28x$

Combine like terms:

$28x - 7 = 28x - 7$

Just like in the first equation, you can see that both sides of the equation are the same. This equation also has infinitely many solutions. Any value of $x$ will satisfy the equation.

In both cases, the solutions are not unique, indicating that the original equations are dependent and have multiple solutions.