Question

Help solving please, I need the full process please

Answer 1

g = 13/4 or 3.25

Explanation:

Step 1: First we can distribute the 2 on the right-hand side (rhs) of the equation:

`(2*5-2*g)/(3)\\\\ (10-2g)/(3)`

Step 2: We can also rewrite this fraction since we have two inverse operations, namely multiplication and division:

`(10)/(3)+(-2g)/(3)\\ \\ (10)/(3)-(2g)/(3)\\ \\ (10)/(3)-(2)/(3)g`

Step 3: We can convert both sides into whole numbers by multiplying both sides by the least common denominator (lcd), which is essentially the lowest multiple shared by the denominators 6 and 3.

The lowest multiple shared by the two numbers is 6 as 6*1 = 6 and 3*2 = 6

Thus, we multiply both sides by 6:

left-hand side (lhs)

`(7)/(6)*(6)/(1)\\ \\ (42)/(6)\\ \\ 7`

right-hand side (rhs)

`((10)/(3)-(2)/(3)g)*(6)/(1)\\ \\ ((10)/(3)*(6)/(1))+(-(2)/(3)g*(6)/(1))\\ \\ (60)/(3)-(12)/(3)g\\ \\ 20-4g`

Since we have simplified both sides, we can now solve for g:

`(7=20-4g)-20\\(-13=-4g)/-4\\13/4=g\\3.25=g`

You can keep the mixed number or use the decimal answer as both are the same answer in different forms.

For such a problem, it can be helpful to check by plugging in 3.25 for g in the equation

`(7)/(6)=(2(5-3.25))/(3)\\ \\ (7)/(6)=(2(1.75))/(3)\\ \\ (7)/(6)=(3.5)/(3)\\\\ 1.167=1.167`