Question

How do you solve `5( x + 1) = 7- 2( 5x + 8)`?

Answer 1

By the usual algebraic manipulations, we get `x = -14/15.`

Explanation:

`5(x+1)=7 -2(5x+8)`

First let's distribute the constant factors:

`5 x + 5 = 7 - (10 x + 16)`

Now we subtract:

`5x + 5 = - 9 - 10 x`

Now we move all the x terms to one side and the constant terms to the other. Terms negate when they move to the other side because what we're really doing is adding the negative to both sides:

`5x + 10 x = -9 - 5`

Now we add and subtract:

`15 x = -14`

Now we divide both sides by 15 for our solution:

`x = -14/15`

Check:

`5(-14/15 + 1) = 5/15 = 1/3`

`7 - 2(5(-14/15) +8) =7 - 2(-14/3 + 24/3)` `= 7 - 2(10/3) = 1/3 quad sqrt`