Finding the value of x

[Probability]

OK tried this all night to solve and not getting anywhere.

- 1/3x + 13/3 = - 2x - 4

First method

12x/3 = - 2x - 4

4x = - 2x - 4

2x = - 4 (NO)

Second method

-1/3x + 13/3 = - 2x - 4

multiply through by 3

-3x + 13 = - 6x - 12

- 9x = 1 (NO)

Third method

-1/3x + 13/3 = -2x -4

-1x + 13 = -6x - 12

-7x = 1 (NO)

I should get x = -5

OK I think I have solved it?

- 1/3x + 13/3 = - 2x - 4

- x + 13 = - 6x - 12

x - x + 13 = - 6x + x - 12

13 = - 5x - 12

13 + 12 = - 5x - 12 + 12

25 = - 5x

x = - 5

 

[JeffM]

OK tried this all night to solve and not getting anywhere.

- 1/3x + 13/3 = - 2x - 4

First method

12x/3 = - 2x - 4

NO $\displaystyle \dfrac{1}{3}x + \dfrac{13}{3} = - 2x - 4 \implies \dfrac{- x}{3} + \dfrac{13}{3} = - 2x - 4 \implies \dfrac{13 - x}{3} = - 2x - 4.$

4x = - 2x - 4

2x = - 4 (NO)

Second method

-1/3x + 13/3 = - 2x - 4

multiply through by 3

-3x + 13 = - 6x - 12 WHAT!!! How do you multiply 3 * (1/3) * x = 3x.

- 9x = 1 (NO)

Third method

-1/3x + 13/3 = -2x -4

-1x + 13 = -6x - 12

-7x = 1 (NO) OH MY

$\displaystyle -1x + 13 = - 6x - 12 \implies + 6x - 1x + 13 = + 6x - 6x - 12 \implies 5x + 13 = - 12 \implies 5x + 13 - 13 = - 12 - 13 \implies$

$\displaystyle 5x = - 25 \implies x = - 5.$

I should get x = -5

Be careful.

 

[Probability]

Be careful.

Thanks Jeff