Solve the equation. Check each solution by substituting it back into the original equation before submitting your quick check.
(g + 4) – 3g = 1 + g
(1 point)
Responses
g = 1
g = 1
g = 4
g = 4
no solution
no solution
identity
g = 1
Checking:
(1 + 4) - 3(1) = 5 - 3 = 2 which is not equal to 1 + 1 = 2.
Therefore, g = 1 is not a solution to the equation.
g = 4
Checking:
(4 + 4) - 3(4) = 8 - 12 = -4 which is not equal to 1 + 4 = 5.
Therefore, g = 4 is not a solution to the equation.
There is no solution to the equation.
To solve the equation (g + 4) - 3g = 1 + g, we can follow these steps:
1. Distribute the negative sign to both terms inside the parentheses:
g + 4 - 3g = 1 + g
2. Combine like terms on each side of the equation:
g - 3g + 4 = 1 + g
3. Simplify the equation by combining like terms:
-2g + 4 = 1 + g
4. Move all the terms containing g to one side of the equation by adding 2g to both sides:
-2g + 2g + 4 = 1 + g + 2g
4 = 1 + 3g
5. Move the constant term to the other side by subtracting 1 from both sides:
4 - 1 = 1 + 3g - 1
3 = 3g
6. Divide both sides by the coefficient of g, which is 3, to solve for g:
g = 3/3
g = 1
To check if the solution is correct, substitute g = 1 back into the original equation:
(g + 4) - 3g = 1 + g
(1 + 4) - 3(1) = 1 + 1
5 - 3 = 2
2 = 2
Since the left side of the equation is equal to the right side when g = 1, the solution is correct.
Therefore, the solution to the equation (g + 4) - 3g = 1 + g is g = 1.
To solve the equation (g + 4) – 3g = 1 + g, we need to simplify and isolate the variable g.
First, let's simplify the equation by removing the parentheses:
g + 4 - 3g = 1 + g.
Next, combine like terms:
4 - 3g = 1 + g.
To isolate the variable g, we can move all the terms with g to one side of the equation and all the constants to the other side. Let's start by moving the g terms to the left side:
4 - 3g - g = 1 + g - g.
Simplifying both sides further:
4 - 4g = 1.
Next, we can solve for g by isolating it. Let's subtract 4 from both sides of the equation:
4 - 4g - 4 = 1 - 4.
Simplifying:
-4g = -3.
Finally, to solve for g, we divide both sides of the equation by -4:
g = -3 / -4.
Simplifying further:
g = 3/4.
Now, to check this solution, substitute it back into the original equation:
(g + 4) – 3g = 1 +g.
Replace g with 3/4:
(3/4 + 4) – 3(3/4) = 1 + 3/4.
Simplifying:
(15/4 ) – 9/4 = 4/4 + 3/4.
Simplifying further:
6/4 = 7/4.
Since 6/4 is equal to 7/4, the solution g = 3/4 satisfies the original equation.
Therefore, the solution to the equation is g = 3/4.