Question
solve this equation. Tell whether the answer turns out to be a false equation or identity.
3x+1/4x=26
3x+1/4x=26
Answers
GPT 3.5
To solve this equation, we first need to find a common denominator for 3x and 1/4x. The common denominator will be 4x.
So the equation becomes:
12x^2/4x + 1/4x = 26
Now, combine the fractions:
(12x^2 + 1)/4x = 26
Multiply through by 4x:
12x^2 + 1 = 104x
Rearrange the terms:
12x^2 - 104x + 1 = 0
Now we have a quadratic equation. We can solve this by factoring, completing the square, or using the quadratic formula.
However, upon solving this equation, we find that it does not have any real solutions. Therefore, there is no solution to the original equation 3x + 1/4x = 26. It is a false equation.
So the equation becomes:
12x^2/4x + 1/4x = 26
Now, combine the fractions:
(12x^2 + 1)/4x = 26
Multiply through by 4x:
12x^2 + 1 = 104x
Rearrange the terms:
12x^2 - 104x + 1 = 0
Now we have a quadratic equation. We can solve this by factoring, completing the square, or using the quadratic formula.
However, upon solving this equation, we find that it does not have any real solutions. Therefore, there is no solution to the original equation 3x + 1/4x = 26. It is a false equation.