14. 9(y - 4) - 7y = 5(3y - 2
step by step please

y=-2

Step-by-step explanation:

Simplifying

9(y + -4) + -7y = 5(3y + -2)

Reorder the terms:

9(-4 + y) + -7y = 5(3y + -2)

(-4 * 9 + y * 9) + -7y = 5(3y + -2)

(-36 + 9y) + -7y = 5(3y + -2)

Combine like terms: 9y + -7y = 2y

-36 + 2y = 5(3y + -2)

Reorder the terms:

-36 + 2y = 5(-2 + 3y)

-36 + 2y = (-2 * 5 + 3y * 5)

-36 + 2y = (-10 + 15y)

Solving

-36 + 2y = -10 + 15y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-15y' to each side of the equation.

-36 + 2y + -15y = -10 + 15y + -15y

Combine like terms: 2y + -15y = -13y

-36 + -13y = -10 + 15y + -15y

Combine like terms: 15y + -15y = 0

-36 + -13y = -10 + 0

-36 + -13y = -10

Add '36' to each side of the equation.

-36 + 36 + -13y = -10 + 36

Combine like terms: -36 + 36 = 0

0 + -13y = -10 + 36

-13y = -10 + 36

Combine like terms: -10 + 36 = 26

-13y = 26

Divide each side by '-13'.

y = -2

Simplifying

y = -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°