Answer:
Using ∣x∣>a⇒x<−a or x>a, we get
∣3x−7∣>4⇒3x−7<−4 or 3x−7>4
⇒3x<3 or 3x>11⇒x<1 or x>
3
11
⇒x∈(−∞,1)∪(
3
11
,∞).
The system of equations have no solution.
Explanation:
The equations are
and 
To find the two numbers, let us solve the equations using substitution method.
From the equation
, let us determine the value of r,

Let us substitute the value of r in
, we get,

which is not possible.
This means that the system has no solution.
A) The longest horizontal distance is reached at 45 degrees angle. This is true for any projectile launch.
B) First, calculate fligth time (using the vertical motion) and then calculate the horizontal movement.
Flight time = 2* ascendent time
ascendent time => final vertical velocity, Vy, = 0
sin(45) = Voy / Vo => Voy = Vosin(45) = 25.5 m/s * (√2) / 2 = 18.03 m/s
Vy = Voy - gt = 0 => Voy = gt = t = Voy / g
Use g = 10 m/s^ (it is an aproximation, because the actual value is about 9.81 m/s^2 depending on the latitud)
t = 18.03 m/s / 10 m/s^2 = 1.83 s
This is the ascendant time going upward.
The flight time is 2*1.83 = 3.66 s
Horizontal motion
Horizontal velocity = Vx = constant = Vox = Vo*cos(45) = 18.03 m/s
Vx = x / t => x = Vx*t
Horizontal distance = xmax = 18.03m/s*3.66 s = 65.99 m
c) The time the ballon will be in the air was calculated in the part B, it is 18.03 s