Respuesta :

nabeelahmed1721

Answer:

6. The number is [tex]-5[/tex]

7. The two numbers are [tex]10[/tex] and [tex]11[/tex]

Step-by-step explanation:

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

[tex]-2=\frac{4x+10}{5}[/tex]

Solve for x to find the number:

[tex]-2=\frac{4x+10}{5}\\-10=4x+10\\-20=4x\\\frac{-20}{4} = x\\-5 = x[/tex]

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. [tex]x + 1 = y[/tex]
  3. [tex]3x - 8 = 2y[/tex]

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

[tex]y = x+1[/tex]

[tex]2y = 3x-8\\y = \frac{3}{2}x - 4[/tex]

Solve for [tex]x[/tex]:

[tex]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[/tex]

Solve for [tex]y[/tex]:

[tex]y = x + 1\\y = 10 + 1\\y= 11[/tex]

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

[tex]\frac{4n+10}{5}[/tex] = - 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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