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boyakko [2]
1 year ago
10

Please help with 6 and 7

Mathematics
2 answers:
Ilya [14]1 year ago
4 0

Answer:

6. The number is -5

7. The two numbers are 10 and 11

Step-by-step explanation:

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

-2=\frac{4x+10}{5}

Solve for x to find the number:

-2=\frac{4x+10}{5}\\-10=4x+10\\-20=4x\\\frac{-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 = \frac{3}{2}x - 4

Solve for x:

x+ 1 = \frac{3}{2}x - 4\\x + 5 = \frac{3}{2}x\\5 = \frac{3}{2}x - x\\5 = \frac{1}{2}x\\10 = x

Solve for y:

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

RideAnS [48]1 year ago
4 0

Answer:

see explanation

Step-by-step explanation:

(6)

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

so

\frac{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

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