Solve the equation. Check your solution.

2g + 3(-5 + 3g) =​1 - g

1 answer

First, let's simplify the equation by distributing the 3 to both terms inside the parentheses:

2g + 3(-5) + 3(3g) = 1 - g

This simplifies to:

2g - 15 + 9g = 1 - g

Combine the like terms:

11g - 15 = 1 - g

Next, let's isolate the variable terms by adding g to both sides:

11g + g - 15 = 1 - g + g

This simplifies to:

12g - 15 = 1

Now, let's isolate the g term by adding 15 to both sides:

12g - 15 + 15 = 1 + 15

This simplifies to:

12g = 16

Finally, divide both sides by 12 to solve for g:

g = 16/12

Simplifying the fraction gives:

g = 4/3

Now, let's check our solution by substituting g = 4/3 back into the original equation:

2g + 3(-5 + 3g) = 1 - g

Substituting g = 4/3:

2(4/3) + 3(-5 + 3(4/3)) = 1 - (4/3)

Simplifying each term:

8/3 + 3(-5 + 4) = 1 - 4/3
8/3 + 3(-1) = 1 - 4/3
8/3 - 3 = 1 - 4/3
8/3 - 9/3 = 1 - 4/3
(-1/3) = 3/3 - 4/3
(-1/3) = -1/3

Both sides of the equation are equal, so the solution g = 4/3 is correct.