x/3 = 4/ x + 1
Is the right side (4/x) + 1 or 4/(x+1) ?
If the latter,
x(x+1) = 12
x^2 +x -12 =0
(x+4)(x-3) = 0
x = 3 or -4
x+y=6
x+3y=6
What is the solution? Select the correct choice below and fill in any answer boxes in your choice.
A__(Type an ordered pair.)
B__There are infinitely many solutions.
C__There is no solution.
To solve this equation, we need to isolate the variable x by getting rid of any fractions. Here's how we can proceed:
Step 1: Multiply both sides of the equation by 3 to eliminate the fraction:
3 * (x/3) = 3 * (4/x + 1)
Simplifying the equation gives:
x = 12/x + 3
Step 2: Multiply both sides of the equation by x to eliminate the fraction:
x * x = 12 + 3x
This leads to:
x^2 = 12 + 3x
Step 3: Move all the terms to one side of the equation to form a quadratic equation:
x^2 - 3x - 12 = 0
Step 4: Factor the quadratic equation, if possible:
(x - 4)(x + 3) = 0
Step 5: Set each factor equal to zero and solve for x:
First factor:
x - 4 = 0
x = 4
Second factor:
x + 3 = 0
x = -3
So, the possible values for x, which are the solutions to the equation, are x = 4 and x = -3.