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Question
In the equation, what is the value of x?
−4(x + 4x) = 2(2 − x) + 10
Responses
A −79
− 7 9
B −97
− 9 7
C 79
7 9
D 97
To find the value of x in the equation, we need to simplify both sides of the equation:
−4(x + 4x) = 2(2 − x) + 10
On the left side, we can distribute the -4 to both terms inside the parenthesis:
-4x - 16x = 2(2 − x) + 10
Simplifying further, we combine like terms on the left side:
-20x = 2(2 − x) + 10
On the right side, we distribute the 2:
-20x = 4 - 2x + 10
Combining like terms on the right side:
-20x = 14 - 2x
To isolate the x term, we can add 2x to both sides:
-20x + 2x = 14 - 2x + 2x
Simplifying:
-18x = 14
Finally, to solve for x, we divide both sides by -18:
x = 14/(-18)
This simplifies to:
x = -7/9
So the value of x is - 7/9.
Therefore, the correct response is B: - 7 9.