Struggling to find the correct mathematical way to find value of x

[Probability]

\(\displaystyle - 1/3x + 13/3 = - 2x - 4\(\displaystyle

I know the value of x = -5 but all the methods I have tried are either -3 or -4.

I am confident it would not be a written error because if I put the x value into the above equations they both balance out with the same answer, so it must be a branch of algebra that I have not yet seen to solve this type of problem.

Any help greatly received.\)\)

 

[soroban]

Hello, Probability!

If you showed your work, we could point out your errors.

\(\displaystyle -\frac{1}{3}x + \frac{13}{3} \:=\:- 2x - 4\)

[1] Multiply by 3: .\(\displaystyle -x + 13 \:=\:-6x - 12 \quad\Rightarrow\quad 5x \:=\:-25 \quad\Rightarrow\quad x \:=\:-5\)


\(\displaystyle [2]\;\;2x-\frac{1}{3}x \:=\:\text{-}4 - \frac{13}{3}\)

. . . . . . .\(\displaystyle \frac{5}{3}x \:=\:\text{-}\frac{25}{3}\)

. . . . . . . ..\(\displaystyle x \:=\:\dfrac{\text{-}\frac{25}{3}}{\frac{5}{3}} \:=\:\left(\text{-}\frac{25}{3}\right)\left(\frac{3}{5}\right)\)

. . . . . . . ..\(\displaystyle x \:=\:\text{-}5\)

 

[Probability]

Hello, Probability!

If you showed your work, we could point out your errors.


[1] Multiply by 3: .\(\displaystyle -x + 13 \:=\:-6x - 12 \quad\Rightarrow\quad 5x \:=\:-25 \quad\Rightarrow\quad x \:=\:-5\)


\(\displaystyle [2]\;\;2x-\frac{1}{3}x \:=\:\text{-}4 - \frac{13}{3}\)

. . . . . . .\(\displaystyle \frac{5}{3}x \:=\:\text{-}\frac{25}{3}\)

. . . . . . . ..\(\displaystyle x \:=\:\dfrac{\text{-}\frac{25}{3}}{\frac{5}{3}} \:=\:\left(\text{-}\frac{25}{3}\right)\left(\frac{3}{5}\right)\)

. . . . . . . ..\(\displaystyle x \:=\:\text{-}5\)

Thanks Soroban you have help a lot with the above. Next time I will include methods I have used to help show where I am going wrong.