One month, ruby worked 6 hours more then isaac, and shetland worked 4 times as many hours as rudy. together they worked 126 hours. find the number of hours each person worked

If we assume the number of hours Isaac worked is x hours. So in that case the number of hours Ruby worked must be 6 + x. And similarly Shetland worked around 4 (6+x) hours.

So we can easily form an expression that gives us how many hours each worked. So basically x + 6 + x + 24 + 4x = 126. So 6x = 96/6 = 16.

SO Isaac worked for 16 hours. Rudy worked for 22 and Shetland worked for the rest.

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 .

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct