Solve for x.

3/7X+ 1/3x = 32

X = ?

3/7x+1/3x=32

We move all terms to the left:

3/7x+1/3x-(32)=0

Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R

Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R

We calculate fractions

9x/21x^2+7x/21x^2-32=0

We multiply all the terms by the denominator

9x+7x-32*21x^2=0

We add all the numbers together, and all the variables

16x-32*21x^2=0

Wy multiply elements

-672x^2+16x=0

a = -672; b = 16; c = 0;

Δ = b2-4ac

Δ = 162-4·(-672)·0

Δ = 256

The delta value is higher than zero, so the equation has two solutions

We use following formulas to calculate our solutions:

x1=−b−Δ√2ax2=−b+Δ√2a

Δ−−√=256−−−√=16

x1=−b−Δ√2a=−(16)−162∗−672=−32−1344=1/42

x2=−b+Δ√2a=−(16)+162∗−672=0−1344=0

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

answer: the correct one is a

step-by-step explanation: