Question

Solve for \(x\) in the equation a(x) = 3x + 1 and (x)=1/x-4

a) \(4\)
b) \(0\)
c) \(1\)
d) \([infinity]\)

Answer 1

To solve the equation a(x) = 3x + 1 and (x)=1/x-4, substitute the second equation into the first equation and solve the resulting quadratic equation.

Step-by-step explanation:

To solve the equation a(x) = 3x + 1 and (x)=1/x-4, we need to find the value of x that satisfies both equations. First, substitute the second equation into the first equation:

a(x) = 3x + 1 = 1/(x - 4)

Next, multiply both sides by (x - 4) to eliminate the fraction:

(x - 4)(3x + 1) = 1

Expand and simplify:

3x^2 - 11x - 4 = 1

Now, move all terms to one side to form a quadratic equation:

3x^2 - 11x - 5 = 0

Finally, solve this quadratic equation using factoring, completing the square, or the quadratic formula to find the values of x.