Question

What is the value of x that makes the given equation true?2(x−8)=x+5x x=−4x=−16x=−2x = 0

Answer 1

As per given by the question,

There are given that a equation,

`2(x-8)=x+5x`

Now,

Solve the given equation to find the value of x, where make the given equation true

`\begin{gathered} 2(x-8)=x+5x \\ 2x-16=6x \\ 2x-16-6x=6x-6x \\ 2x-16-6x=0 \\ -4x-16=0 \\ -4x=16 \end{gathered}`

Now,

divide by 4 on both side of the equation

Then,

`\begin{gathered} -4x=16 \\ -(4x)/(4)=(16)/(4) \\ x=-4 \end{gathered}`

Then,

Put the value of x into the given equation, to check that the given equation is true at x=-4.

So,

`\begin{gathered} 2(x-8)=x+5x \\ 2(-4-8)=-4+5(-4) \\ 2(-12)=-4-20 \\ -24=-24 \end{gathered}`

Hence, the given equation is true at the point x=-4.

So,

The option A is correct.