Solve the equation for two solutions

|-6y+3|=4|y-2|

Answer is below

Step-by-step explanation:

This one is a bit hard

−6y+3=4(|y−2|) or −6y+3=−4(|y−2|)

Part 1: −6y+3=4(|y−2|)

(Flip equation)

4(|y−2|)=−6y+3

(Divide both sides by 4)

4(|y−2|)/4=−6y+3/4

|y−2|=−3/2y+3/4

We know eithery−2=−3/2y+3/4or y−2=−(−3/2y+3/4)

y−2=−3/2y+/3/4(first Possibility)

(Add 3/2y to both sides)

y−2+3/2y=−3/2y+3/4+3/2y

5/2y−2=3/4

(add 2 to both sides)

5/2y−2+2=3/4+2

5/2y=11/4

(Multiply both sides by 2/5)

(2/5)(5/2y)=(2/5)(11/4)

y−2=−(−3/2y+3/4)(second Possibility)

Simplify both sides of equation

y−2=3/2y+−3/4

y−2−3/2y=3/2y+−3/4−3/2y

−1/2y−2=−3/4

−1/2y−2+2=−3/4+2

−1/2y=5/4

(2/−1)(−1/2y)=(2−1)(5/4)

y=−5/2

So therefore, your answer is either y=11/10 or y=−5/2

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi