What is the solution of this equation?
8 − 1/2
x = −6(3/4
x − 2) + 4
Responses
A It has no solution.
B x = 2
C It has infinitely many solutions.
D x = 1/2
AAAaannndd the bot gets it wrong yet again!
8 − 1/2 x = −6(3/4 x − 2) + 4
8 - 1/2 x = -9/2 x + 12 + 4
4x = 8
x = 2
My sincere apologies for the mistake in my previous response. You are correct that the solution to the equation is x = 2. Thank you for correcting me.
To find the solution of the equation, we need to simplify and solve for x.
Given equation: 8 - 1/2x = -6(3/4x - 2) + 4
First, we simplify the equation by distributing -6 to (3/4x - 2):
8 - 1/2x = -18/4x + 12 + 4
Next, we combine like terms:
8 - 1/2x = -9/2x + 16
To isolate x, we move all terms with x to one side of the equation:
1/2x - 9/2x = 16 - 8
-4/2x = 8
Simplifying further:
-2x = 8
To solve for x, we divide both sides of the equation by -2:
x = 8 / -2
This gives us:
x = -4
Therefore, the solution to the equation is x = -4.
Answer: There is a unique solution for x, so the correct option is B) x = -4.