Solve: x+4/4 = x/x-2 answers are {-4,2}

x=4                         x=-2

Step-by-step explanation:

x+4                  x

=

4                  x-2

Using cross products

(x+4)(x-2) = 4x

FOIL

x^2 -2x +4x -8 = 4x

Combine like terms

x^2 +2x -8 = 4x

Subtract 4x from each side

x^2 +2x-4x -8 = 4x-4x

x^2 -2x-8 =0

Factor

What 2 numbers multiply to -8 and add to -2

-4*2 =-8

-4+2 = -2

(x-4) (x+2) =0

Using the zero product property

x-4+4 =0+4         x+2-2=0-2

x=4                         x=-2

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°