What is the answer negative one times the sum of one and seven times a number, decreased by 6 times the difference of negative seven and a number, equals thirty-six

The number is -79.

Step-by-step explanation:

Let's set up equation for the given information.

Let the number as 'x'

Negative 1 times the sum of one and seven times a number x could be written as -1(1+7 x).

Now, 6 times the difference of negative seven and a number could be written as

6(-7-x)

Now,

-1(1+7 x) decreased by 6(-7-x) equals 36

So, we can set up equation as

-1(1+7 x)-6(-7-x)=36

Solve the equation for x

-1-7 x-42+6 x=36

Combine like terms

-x-43 =36

Add both sides 43

-x=79

Divide both sides by -1.

x=79

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .