Question

How do you solve `17= - 2x - 3+ 7x`?

Answer 1

Combine like terms, rearrange, and then solve for `x` to find `x=4`

Explanation:

First, lets combine like terms on the Right-Hand Side (RHS). We have two numbers that are both multiplied by `x`, so we can group them like so:

`17=-2x-3+7x`

`17=-3+7x-2x`

`17=-3+x(7-2)`

`17=-3+5x`

Next, we'll re-arrange the equation to get `x` and its coefficient by itself, on the RHS. We'll achieve this by adding 3 to both sides, which will eliminate the -3 on the RHS, and effectively moving it to the Left-Hand Side (LHS):

`17color(red)(+3)=cancel(-3)+5xcolor(red)(cancel(+3))`

`20=5x`

Finally, we'll divide both sides by the coefficient that `x` is multiplied by, which should give us our answer:

`20/color(red)(5)=(cancel(5)x)/color(red)(cancel(5))`

`color(green)(x=4)`

Answer 2

`x=4`

Explanation:

`17=-2x-3+7x`

can also be written as

`17=5x-3`

To solve this, you want all of the `x`'s on one side of the equation: Therefore, you can add `3` to both sides to make;

`20=5x`

To get `x` on its own, you then divide both sides by `5` to get:

`4=x`

Answer 3

X = 4

Explanation:

Given:

`17 = -2x-3+7x`

Adding 3 to both sides,
`17+3 = cancel(3)-cancel(3)+ 5x`
`20 = 5x`

Dividing both sides with 5, we get,
`cancel(20)/cancel(5) = cancel(5)/cancel(5)x`
`:.x = color(red)(4)`