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Question
Which graph represents the solution for the equation 3x + 4 = -2x - 2?
Responses
A
B
C
D
To find which graph represents the solution for the equation 3x + 4 = -2x - 2, we need to solve the equation and analyze the options.
First, let's solve the equation:
3x + 4 = -2x - 2
Combining like terms:
3x + 2x = -2 - 4
5x = -6
Dividing both sides by 5:
x = -6/5
Now, let's analyze the options to see which graph represents this solution.
Since we found x = -6/5, we can substitute this value into the equation to see if it matches the options:
For option A -> 3(-6/5) + 4 = -2(-6/5) - 2
Simplifying, we get: -18/5 + 4 = 12/5 - 2
This is not true, so option A is not the correct graph.
For option B -> 3(-6/5) + 4 = -2(-6/5) - 2
Simplifying, we get: -18/5 + 4 = 12/5 - 2
This is also not true, so option B is not the correct graph.
For option C -> 3(-6/5) + 4 = -2(-6/5) - 2
Simplifying, we get: -18/5 + 4 = 12/5 - 2
This is still not true, so option C is not the correct graph.
For option D -> 3(-6/5) + 4 = -2(-6/5) - 2
Simplifying, we get: -18/5 + 4 = 12/5 - 2
This is true, since both sides of the equation are equal.
Therefore, the graph that represents the solution for the equation 3x + 4 = -2x - 2 is option D.