Question

Solve for x-10/x= -16/x+3I'm having issues figuring this problem out. Could you please explain.

Answer 1

x = 5

Step-by-step explanation

`(-10)/(x)=(-16)/(x+3)`

To solve this, we need x to be in the numerator of each fraction. To do that, we can multiply both sides by x:

`\begin{gathered} (-10)/(x)\cdot x=(-16)/(x+3)\cdot x \\ -10=(-16x)/(x+3) \end{gathered}`

And also multiply both sides by (x+3):

`\begin{gathered} -10(x+3)=(-16x)/(x+3)(x+3) \\ -10(x+3)=-16x \end{gathered}`

And now we have a very simple linear equation to solve.

First we have to distribute -10 into the sum inside the parenthesis:

`-10x-30=-16x`

Now we add 16x on both sides of the equation:

`\begin{gathered} -10x+16x-30=-16x+16x \\ 6x-30=0 \end{gathered}`

Add 30 on both sides:

`\begin{gathered} 6x-30+30=30 \\ 6x=30 \end{gathered}`

And finally divide both sides by 6:

`\begin{gathered} (6x)/(6)=(30)/(6) \\ x=5 \end{gathered}`