21−7xx−3=x21-7𝑥𝑥-3=𝑥 What is the negative solution to the given equation?

To find the negative solution to the equation 21 - 7x / x - 3 = x, follow these steps:

Step 1: Simplify the equation by multiplying every term by (x - 3) to get rid of the denominator. This gives us:

21(x - 3) - 7x = x(x - 3)

Step 2: Distribute the terms on both sides of the equation:

21x - 63 - 7x = x^2 - 3x

Step 3: Simplify the equation by combining like terms:

14x - 63 = x^2 - 3x

Step 4: Rearrange the equation to set it equal to zero:

x^2 - 3x - 14x + 63 = 0

Step 5: Simplify the equation:

x^2 - 17x + 63 = 0

Step 6: Factor the quadratic equation:

(x - 9)(x - 7) = 0

Step 7: Set each factor equal to zero and solve for x:

x - 9 = 0 => x = 9 x - 7 = 0 => x = 7

The solutions to the equation are x = 9 and x = 7. However, the question asks for the negative solution. Since neither of these solutions are negative, there is no negative solution to the given equation.