Question

How do you solve `3a + (2a - 5) = 13 - 2(a + 2 )`?

Answer 1

`a=14/7`

Explanation:

`3a+(2a-5)=13-2(a+2)`
`3a+(2a-5)=13-(2a+4)`
`3a+2a-5=13-2a-4`
`5a-5=9-2a`
`5a+2a=9+5`
`7a=14`
`a=14/7`

Answer 2

`a=2`

Explanation:

`"distribute parenthesis on both sides of the equation"`

`3a+2a-5=13-2a-4`

`"collect like terms on both sides"`

`rArr5a-5=9-2a`

`"add 2a to both sides"`

`5a+2a-5=9cancel(-2a)cancel(+2a)`

`rArr7a-5=9`

`"add 5 to both sides"`

`7acancel(-5)cancel(+5)=9+5`

`rArr7a=14`

`"divide both sides by 7"`

`(cancel(7) a)/cancel(7)=14/7`

`rArra=2`

`color(blue)"As a check"`

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

`"left "=6+(-1)=6-1=5`

`"right "=13-2(4)=13-8=5`

`rArra=2" is the solution"`