Question

Please help with 6 and 7

Answer 1

see explanation

Explanation:

(6)

let n be the number then the sum of 4 times the number and 10 is 4n + 10

so

`(4n+10)/(5)` = - 2 ( multiply both sides by 5 to clear the fraction )

4n + 10 = - 10 ( subtract 10 from both sides )

4n = - 20 ( divide both sides by 4 )

n = - 5

(7)

let the consecutive integers be n and n + 1 , then

3n = 2(n + 1) - 8 ← distribute parenthesis and simplify right side

3n = 2n + 2 - 8

3n = 2n - 6 ( subtract 2n from both sides )

n = - 6 and n + 1 = - 6 + 1 = - 5

the 2 integers are - 6 and - 5

Answer 2

6. The number is
`-5`

7. The two numbers are
`10` and
`11`

Explanation:

Question six can be re-worded to create the following expression:

`-2=(4x+10)/(5)`

Solve for x to find the number:

`-2=(4x+10)/(5)\\-10=4x+10\\-20=4x\\(-20)/(4) = x\\-5 = x`

Question seven can be solved by first listing the constraints (assuming x is smaller than y):

1. x and y are less than 20
2. 
   `x + 1 = y`
3. 
   `3x - 8 = 2y`

To get the numbers, we can create a system of linear equations. First, solve for
`y` in each expression:

`y = x+1`

`2y = 3x-8\\y = (3)/(2)x - 4`

Solve for
`x`:

`x+ 1 = (3)/(2)x - 4\\x + 5 = (3)/(2)x\\5 = (3)/(2)x - x\\5 = (1)/(2)x\\10 = x`

Solve for
`y`:

`y = x + 1\\y = 10 + 1\\y= 11`