Multiple Choice
(g + 4) – 3g = 1 + g
(1 point)
Responses
1
1
4
4
no solution
no solution
identity
identity
no solution
To solve the given equation, we can start by simplifying both sides of the equation and combining like terms:
(g + 4) - 3g = 1 + g
First, distribute the negative sign to the terms inside the parentheses:
g + 4 - 3g = 1 + g
Next, collect like terms on both sides of the equation:
g - 3g + 4 = g + 1
Combine similar terms:
-2g + 4 = g + 1
Now, let's isolate g by moving all terms with g to one side of the equation and the constants to the other side:
-2g - g = 1 - 4
Simplify:
-3g = -3
Finally, divide both sides of the equation by -3 to solve for g:
g = -3 / -3
This simplifies to:
g = 1
So, the correct response is:
1
To solve the equation (g + 4) – 3g = 1 + g, you can follow these steps:
Step 1: Distribute the subtraction sign to both terms inside the parentheses.
g + 4 - 3g = 1 + g
Step 2: Combine like terms on both sides of the equation.
-2g + 4 = 1 + g
Step 3: Move all terms involving g to one side of the equation by subtracting g from both sides.
-2g - g + 4 = 1
Step 4: Combine like terms on the left side of the equation.
-3g + 4 = 1
Step 5: Move the constant term to the other side of the equation by subtracting 4 from both sides.
-3g = 1 - 4
Step 6: Simplify the right side of the equation.
-3g = -3
Step 7: Solve for g by dividing both sides of the equation by -3.
g = -3 / -3
Step 8: Simplify the fraction.
g = 1
So, the solution to the equation is g = 1.
Therefore, the answer is 1.
5y + 2 = one half(10y + 4)
(1 point)
Responses
5
5
10
10
no solution
no solution
identity
To solve the given equation, we can start by simplifying both sides of the equation:
5y + 2 = (1/2)(10y + 4)
First, we can simplify the right side of the equation by distributing (1/2) to both terms inside the parentheses:
5y + 2 = (1/2)(10y) + (1/2)(4)
5y + 2 = 5y + 2
Notice that both sides of the equation are identical! This means that the equation holds true for any value of y. Therefore, the equation has infinite solutions.
So, the correct response is:
identity
0.5b + 4 = 2(b + 2)
(1 point)
Responses
0
0
0.5
0.5
no solution
no solution
identity
To solve the given equation, we can start by simplifying both sides of the equation:
0.5b + 4 = 2(b + 2)
First, we can distribute 2 to both terms inside the parentheses on the right side:
0.5b + 4 = 2b + 4
Next, let's move all terms involving b to one side of the equation by subtracting 2b from both sides:
0.5b - 2b + 4 = 4
Simplifying the left side, we get:
-1.5b + 4 = 4
Now, let's move the constant term to the other side of the equation by subtracting 4 from both sides:
-1.5b = 4 - 4
Simplifying, we have:
-1.5b = 0
To solve for b, we divide both sides of the equation by -1.5:
b = 0 / -1.5
Simplifying the fraction, we get:
b = 0
So, the solution to the equation is b = 0.
Therefore, the correct response is:
0
–3x + 5 = –3x + 10
(1 point)
Responses
5/6
Image with alt text: 5/6
–5/6
– Image with alt text: 5/6
no solution
no solution
identity
To solve the given equation, we can start by simplifying both sides of the equation:
-3x + 5 = -3x + 10
Notice that the variable term (-3x) appears on both sides of the equation. In this case, we cannot isolate the variable and solve for x because the variable terms cancel each other out.
If we subtract -3x from both sides of the equation, we would be left with:
5 = 10
This is a nonsensical statement since 5 is not equal to 10.
Therefore, the equation has no solution.
So, the correct response is:
no solution