I REALLY need help! Solve the inequality. State the solution in inequality notation. 2(3x−4)+14>−2(−3x−5)+4x

x<−1

Step-by-step explanation:

x < -1

2(3x - 4) + 14 > -2(-3x - 5) + 4x

<=> 6x - 8 + 14 > 2(3x + 5) + 4x

<=> 6x + 6 > 6x + 10 + 4x

<=> 4x + 4 < 0

<=> 4x < -4

<=> x < -1

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

(-5,-28)

i graphed to on desmos.