Question

-4(3x - 5) = -16 - 12x

Answer 1

The algebraic equation -4(3x - 5) = -16 - 12x results in a contradiction when simplified, indicating there is no solution, since it simplifies to 20 = -16, which is not possible.

Step-by-step explanation:

Let's solve the algebraic equation -4(3x - 5) = -16 - 12x. First, distribute the -4 within the parentheses:

-4 × 3x gives us -12x, and -4 × -5 gives us +20.

Thus, the equation becomes:
-12x + 20 = -16 - 12x.

Now, add 12x to both sides of the equation to get rid of the x terms:
20 = -16.

This is a contradiction, which means there is no solution, or the system of equations is inconsistent.

Remember, when two numbers with opposite signs multiply, the answer has a negative sign, such as (-3) × 3 = -9. Also, when two negative numbers multiply, the answer is positive, e.g., (-4) × (-3) = 12.

Answer 2

The question here is to solve for the value of x.

We will use the distributive property to make the left-hand side of the equation easier to work with.

Distributive Property:

`a(b\pm c)=ab\pm ac`

LHS becomes:

`-4\left(3x-5\right)=-4(3x)-4(-5)=-12x+20`

Now the equation becomes:

`-12x+20=-16-12x`

We put all the x's to one side and numbers to another (remember to change signs when changing sides):

`\begin{gathered} -12x+20=-16-12x \\ -12x+12x=-16-20 \\ 0x=-36 \\ 0=-36 \end{gathered}`

Now wait!

It doesn't make sense.

So, this equation is faulty. There is no solution.