Solving for "x" in equation?

Question

Equation: y=(2x-1)/(4x+3) Solve for x.

Solve for "x" in terms of getting of the equation. I'm not looking for a specific number. Sorry.

Answer 1

4xy + 3y = 2x - 1 © cross multiply

4xy - 2x = -3y - 1
x = (-3y - 1)/(4y - 2)

Answer 2

What is a quadratic equation? Quadratic equations can come in many forms: x2 + 19 = 0 4x2 – 2x = 0 3x2 – 2x + 10 = 0 However, they are all in terms of one variable with a degree of 2.The standard form is ax2 + bx + c = 0, but b or c may be 0 as in the first and second equations above. Four Methods for Solving Quadratic Equations Factoring Method. Graphing Method. Square Root Method. Quadratic Formula Method. Why so many? Some quadratics factor easily. Some are easier to graph. If the quadratic equation does not factor then you will not be able to find a solution by factoring or an exact solution on a graph. Then the square root method is used. A short cut for the square root method is the quadratic formula. So, you can see that they all have their uses; it just depends on the problem. The good news is that you have learned the first two previously. In this section we will use the 3rd and 4th techniques listed above, involving square roots. The Square Root Method Binomials in the Form ax2 – c = 0 or ax2 = c. Isolate the x2. Take the square root of both sides. Simplify the two solutions. Check by substituting the solutions into the equation.

Answer 3

y=(2x-1)/(4x+3)

Solve the roots of the equation.

1st root:
y = 0, when x = 0.5

2nd root:
y = 0, when x = ∞

Proof of 2nd root using l'Hopital's rule:
i.e, Prove y -> 0 when x -> ∞ .

i.e. prove dy/dx -> 0 when x -> ∞


Let u = 4x + 3
Therefore, y = (u - 5)/2u = 1/2 - 5/u

du/dx = 4
dy/du = 5/u^2
dy/dx = dy/du * du/dx
= 20/(4x + 3)^2

Therefore, dy/dx = 0 when x = ∞ .

Therefore, the roots of the equation are
x = 1/2 and x = infinity.


Notes:
# You cannot use (4x + 3) = 0 to get the 2nd root because it is a denominator. This is not a quadratic equation.

# The usual language is
"Solve the roots of the equation ...."
not
"Solve the equation ..."
if you provided an equation and wanted the values of x when y is 0.
Otherwise, "solve the equation ..." would require two mutually independent equations containing both x and y terms.

Answer 4

assume that y=0, equate (2x-1) to zero which makes it 2x-1=0 which becomes 2x=1 after divide both sides by 2 which makes it 2x/2=1/2; 2x/2=x which makes it x therefore x =1/2 the answer to 4x+3 is x= -3/4

Answer 5

You need to have a second equation to "solve" for x. X is unconstrained in value except that x cannot equal -3/4.

So x is an element of the real or complex numbers and is not equal to -3/4.

Answer 6

rite now youve got one eqn and two variables....

its impossible to solve it/

Answer 7

y=(2x-1)/(4x+3)
y(4x+3)= 2x-1
4xy+3y=2x-1
4xy-2x=-3y-1
x(4y-2)=-3y-1
x=(-3y-1)/(4y-2)