How would you solve for x?

- 6 / (x + 7) = x / 2

<=>

x * (x + 7) = - 6 * 2

<=>

x² + 7x + 12 = 0

Delta = 49 - 48 = 1

x1 = (- 7 - 1) / 2 = - 4

x2 = (- 7 + 1) / 2 = - 3

*******

-6/(x + 7) = x/2
-12 = x(x + 7) = x² + 7x # add 12
x² +7x + 12 = 0
x1 = -3
x2 = -4

-6/(x+7) = x/2
cross multiply
x (x+7) = -12
x^2 +7x +12 = 0
(x + 3) (x + 4) = 0

x+3 = 0
x = -3

x +4 = 0
x = -4

so x values are -3, -4

cross multiply.

-12 = x^2 + 7x
x^2 + 7x + 12 = 0

Use the quadratic formula

(x + 3)(x+4) = 0

x = -3 , -4

-6/(x + 7) = x/2
-6 = (x + 7)(x/2)
-6 = (x^2 + 7x)/2
2(-6) = x^2 + 7x
-12 = x^2 + 7x
x^2 + 7x + 12 = 0
x^2 + 4x + 3x + 12 = 0
(x^2 + 4x) + (3x + 12) = 0
x(x + 4) + 3(x + 4) = 0
(x + 4)(x + 3) = 0

x + 4 = 0
x = -4

x + 3 = 0
x = -3

∴ x = -4, -3

cross multiply to get -12=x^2+7x

add 12 to both sides. your final equation is x^2 +7x +12=0

factor to (x+3)(x+4) answers are -3 and -4

Cross multiply:
x(x+7) = (2)(-6)
x^2+7x = -12
x^2+7x+12 = 0
(x+3)(x+4) = 0
x = -3 or -4

All answer are incorrect or partly appropriate! The is a try in spite of if the equation holds. because of the fact the quotient x/x is given, the equation is defined for x=0, because of the fact the actuality, that there is a real shrink for x goint to 0 of x/x: limit_x->0 x/x=a million. So do away with the quotient a minimum of for x unequal 0. The equation now's x+x²=x². This equation could be rearranged by way of unique arithmetic operations. It provides x=0. stupid or. What does is mean? The equation does no longer carry for x unequal 0. it quite is it. it may returned be simplified a million+x=x or a million=0, that's incorrect. For 0 is holds interior the secure style and interior the shrink attention: 0/0+0=a million+0 unequal 0. The equation does no longer be valid for any authentic numbers!

- 6 / (x + 7) = x / 2
- 12 = x ( x + 7 )
x ² + 7x + 12 = 0
( x + 4 ) ( x + 3 ) = 0
x = - 4 , x = - 3

. . . 6 . . . . x
-——— = —
. .x + 7 . . .2

*cross multiply*

-6(2) = x(x + 7)

-12 = x² + 7x

x² + 7x + 12 = 0

(x + 3)(x + 4) = 0

x = -3, -4


Done