Solve the equation. Check your solution.3g + 4(-6 + 4g) = 1 -g
To solve the equation, we need to simplify both sides and isolate the variable g. Let's go step by step:
First, distribute the 4 to the terms inside the parentheses: 3g + 4(-6) + 4(4g) = 1 - g
It becomes: 3g - 24 + 16g = 1 - g
Next, combine like terms on both sides: 3g + 16g - g = 1 + 24
It becomes: 18g = 25
Now, isolate the variable g by dividing both sides by 18: 18g/18 = 25/18
It becomes: g = 25/18
To check the solution, substitute the value of g back into the original equation:
3g + 4(-6 + 4g) = 1 - g
3(25/18) + 4(-6 + 4(25/18)) = 1 - (25/18)
Simplifying this expression:
75/18 - 4(6) + 4(100/18) = 1 - (25/18)
75/18 - 24 + 400/18 = 1 - (25/18)
(75 - 432)/18 = (18 - 25)/18
Now, simplify both sides further:
-357/18 = -7/18
The left side does not equal the right side. Therefore, the value of g = 25/18 does not satisfy the original equation.
To solve the equation, let's first simplify each side of the equation:
3g + 4(-6 + 4g) = 1 - g
Distribute the 4 on the left side:
3g - 24 + 16g = 1 - g
Combine like terms on the left side:
3g + 16g - 24 = 1 - g
Combine like terms on the right side:
19g - 24 = 1 - g
Now, let's isolate the variable g by adding g to both sides:
19g - 24 + g = 1 - g + g
Combine like terms:
20g - 24 = 1
Next, add 24 to both sides to continue isolating g:
20g - 24 + 24 = 1 + 24
Simplify:
20g = 25
Finally, divide both sides by 20 to solve for g:
g = 25/20
Simplifying the fraction:
g = 5/4 or g = 1.25
To check the solution, substitute the value of g back into the original equation:
3g + 4(-6 + 4g) = 1 - g
Let's check for g = 1.25:
3(1.25) + 4(-6 + 4(1.25)) = 1 - 1.25
Simplify both sides:
3.75 + 4(-6 + 5) = 1 - 1.25
3.75 + 4(-1) = 1 - 1.25
3.75 - 4 = 1 - 1.25
-0.25 = -0.25
Since both sides of the equation are equal, the solution g = 1.25 is correct.