Multiple Choice
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
no solution
To solve the equation (g + 4) - 3g = 1 + g, we can follow these steps:
Step 1: Distribute the positive/negative sign to simplify the equation.
(g + 4) - 3g = 1 + g
g + 4 - 3g = 1 + g
Step 2: Combine like terms.
g - 3g + 4 = 1 + g
Step 3: Simplify further.
-2g + 4 = 1 + g
Step 4: Move all terms with g to one side and constant terms to the other side.
-2g - g = 1 - 4
Step 5: Combine like terms.
-3g = -3
Step 6: Divide both sides by -3 to isolate g.
g = -3 / -3
g = 1
So, the solution to the equation is g = 1.
To check if this solution is correct, substitute g = 1 back into the original equation.
Left-hand side: (g + 4) - 3g
= (1 + 4) - 3(1)
= 5 - 3
= 2
Right-hand side: 1 + g
= 1 + 1
= 2
Since the values for both sides of the equation are equal (2 = 2), the solution g = 1 is correct.
Therefore, the correct response is:
g = 1
To solve the equation (g + 4) – 3g = 1 + g, we can follow these steps:
Step 1: Simplify both sides of the equation.
(g + 4) - 3g = 1 + g
g + 4 - 3g = 1 + g
4 - 3g = 1
Step 2: Combine like terms.
4 - 3g = 1
Step 3: Move all terms involving g to one side of the equation.
-3g - g = 1 - 4
-4g = -3
Step 4: Divide both sides of the equation by -4 to solve for g.
(-4g) / (-4) = (-3) / (-4)
g = 3/4
Now, we need to check if this solution is correct by substituting g = 3/4 back into the original equation.
(g + 4) - 3g = 1 + g
(3/4 + 4) - 3(3/4) = 1 + (3/4)
(3/4 + 16/4) - 9/4 = 4/4 + 3/4
19/4 - 9/4 = 7/4
10/4 = 7/4
The equation is not true for g = 3/4. Therefore, the correct solution is no solution.