Question

`2(1/3 - w)=8/3+12w`

Solve this equation, handwritten if possible.

Answer 1

Bet

Explanation:

w = -1/7

Explanation:

We start with the equation 2(-w) = 1 + 12w.

Distributing the 2 on the left side gives us -2w = 1 + 12w.

Subtracting 36w from both sides gives us -2 - 36w = 1.

Simplifying the left side gives us -38w = 1.

Dividing both sides by -38 gives us w = -1/7.

Here is a more detailed explanation of each step:

Distribute the 2 on the left side. When we multiply a number by a variable, we multiply each term in the variable by the number. In this case, we are multiplying 2 by -w, which gives us -2w.

Subtract 36w from both sides. This eliminates 36w from the equation, leaving us with -2 - 36w on the left side and 1 on the right side.

Simplify the left side. Combining the numeric terms on the left side gives us -38w.

Divide both sides by -38. This gives us w = -1/7.

I hope this is helpful! Let me know if you have any other questions.

Answer 2

w = -
`(1)/(7)`

Explanation:

2(
`(1)/(3)` - w) =
`(8)/(3)` + 12w ← distribute parenthesis on left side by 2

`(2)/(3)` - 2w =
`(8)/(3)` + 12w

multiply through by 3 to clear the fractions

2 - 6w = 8 + 36w ( subtract 36w from both sides )

2 - 6w - 36w = 8 + 36w - 36w ( simplify )

2 - 42w = 8 ( subtract 2 from both sides )

2 - 2 - 42w = 8 - 2 ( simplify )

- 42w = 6 ( divide both sides by - 42 )

`(-42)/(-42)` w =
`(6)/(-42)` , that is

w = -
`(1)/(7)`