Question
solve this equation. Tell whether the problem is a false equation or identity.
-1/4x-4+3/4x=1/2x+1
-1/4x-4+3/4x=1/2x+1
Answers
GPT 3.5
To solve the equation, we first need to add the terms involving x on one side of the equation and the constants on the other. We start by adding 1/4x to both sides of the equation:
-1/4x - 4 + 3/4x = 1/2x + 1
=> 2/4x - 4 = 1/2x + 1
Next, we simplify the equation by converting all fractions to have a common denominator:
=> (2 - 16)/4x = 2/2x + 2
=> -14/4x = 2/2x + 2
Now, we simplify this further by cross-multiplying:
=> -14(2x) = 2(4x) + 2(4x)
=> -28x = 8x + 8x
=> -28x = 16x
At this point, we see that the equation simplifies to -28x = 16x, which is false. Therefore, the given equation -1/4x - 4 + 3/4x = 1/2x + 1 is a false equation.
-1/4x - 4 + 3/4x = 1/2x + 1
=> 2/4x - 4 = 1/2x + 1
Next, we simplify the equation by converting all fractions to have a common denominator:
=> (2 - 16)/4x = 2/2x + 2
=> -14/4x = 2/2x + 2
Now, we simplify this further by cross-multiplying:
=> -14(2x) = 2(4x) + 2(4x)
=> -28x = 8x + 8x
=> -28x = 16x
At this point, we see that the equation simplifies to -28x = 16x, which is false. Therefore, the given equation -1/4x - 4 + 3/4x = 1/2x + 1 is a false equation.