Question

How do you solve `1+ 3a = - 8- 4a`?

Answer 1

`a=-9/7`

Explanation:

`"collect terms in a on the left and numeric values on the "`
`"right side of the equation"`

`"add 4a to both sides"`

`1+3a+4a=-8cancel(-4a)cancel(+4a)`

`rArr1+7a=-8`

`"subtract 1 from both sides"`

`cancel(1)cancel(-1)+7a=-8-1`

`rArr7a=-9`

`"divide both sides by 7"`

`(cancel(7) a)/cancel(7)=(-9)/7`

`rArra=-9/7`

`color(blue)"As a check"`

Substitute this value into the equation and if both sides are equal then it is the solution.

`"left "=7/7-27/7=-20/7`

`"right "=-56/7+36/7=-20/7`

`rArra=-9/7" is the solution"`

Answer 2

`a = -(9)/(7)`

Explanation:

`1+3a=−8−4a`    Solve for `a`

1) Add `4a` to both sides to collect all the `a` terms on the same side.
After you have added, you get this:
`1 + 7a = - 8`

2) Subtract `1` from both sides to isolate the `7a` term
After you subtract, you will have this:
`7a = - 9`

3) Divide both sides by `7` to isolate `a`
`a = -(9)/(7)` `larr` answer

`color(white)(mmmmmmmm)`―――――――――

Check
1) Sub in `-(9)/(7)` in the place of `a` in the original equation

`1+3a=−8−4a`

`1+3(-(9)/(7)) "should equal"−8−4(-(9)/(7))`

2) Clear the parentheses by distributing the coefficients

`1 - (27)/(7)  "should equal" - 8 +(36)/(7)`

3) To add, give the whole numbers the common denominator of `7`

`(7)/(7) - (27)/(7) "should equal" - (56)/(7) +(36)/(7)`

4) Add like terms

`-(20)/(7)  "does equal" - (20)/(7)`

`Check`