Five divided by the difference of a number and 1 equals the quotient of ten and the sum of the number and eleven. find the number.

x=13 (The number is 11)

Step-by-step explanation:

5/(x-1)=10/x+11

Use cross multiplication:

5(x+11)=10(x-1)

5x+55=10x-10

(Rewrite):10x-10=5x+55

Substract 5x from each side then simplify.

10x-5x-10=5x-5x+55

5x-10=0+55

5x-10=55

Add ten on both sides. Then simplify.

5x-10+10=10+55

5x=65

x=13

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 .