Question

What are three consecutive integers such that -4 times the sum of the first and the third is 12 igreater than the product of 7 and the opposite of the second?

Answer 1

The three consecutive integers become

`x = -13`
`x+1 = -12`
`x+2 = -11`

Explanation:

Begin by naming the three consecutive integers as

`x`
`x+1`
`x+2`
therefore the opposite of the second would be
`-x-1`

Now create the equation

`-4(x+x+2) = 7(-x-1) +12`

combine like terms in the ( ) and the distributive property

`-4(2x+2) = -7x-7+12`

use the distributive property

`-8x-8=-7x+5`

use the additive inverse to combine the variable terms

`cancel(-8x) cancel(+8x)-8=-7x +8x+5`

`-8 = x+5`

use the additive inverse to combine the constant terms

`-8 -5 = x cancel(+5) cancel(-5)`

simplify

`-13 = x`