Brainest for right person! question part a: eplain why x = 3 makes 4x − 1 ≤ 11 true but not 4x − 1 < 11. part b: what value from the set {4, 5, 6, 7, 8} makes the equation 8x + 1 = 57 true? question 2 a theater company has raised $870.75 by selling 25 floor seat tickets. each ticket costs the same. part a: write an equation with a variable that can be solved to correctly find the price of each ticket. explain how you created this equation. part b: solve your equation in part a to find the price of each floor seat ticket. how do you know your solution is correct? question 3 a ride in an amusement park has the following notice at the gate: "children under the age of 8 are not allowed on this ride." part a: write an inequality to show the age of children who are allowed on the ride. part b: describe in words how you can show the solution to this inequality on a number line

Part 1) Eplain why x = 3 makes 4x − 1 ≤ 11 true but not 4x − 1 < 11. 

4x − 1 ≤ 11> 4x ≤ 11+1> x≤ 12/4> x ≤  3

the solution for this inequality is the interval (-∞, 3]
the value of 3 is included

in the inequality 
4x − 1 < 11> 4x < 11+1> x< 12/4> x < 3

the solution for this inequality is the interval (-∞, 3)
the value of 3 is not included

Part 2) What value from the set {4, 5, 6, 7, 8} makes the equation 8x + 1 = 57 true?

8x + 1 = 57> 8x=57-1> x=56/8> x=7

the answer Part 2) is
the value from the set that makes the equation true is 7

Part 3) A theater company has raised $870.75 by selling 25 floor seat tickets. Each ticket costs the same. 

 A): Write an equation with a variable that can be solved to correctly find the price of each ticket. Explain how you created this equation.  

let
x> the price for each ticket

we know that
25*x =  $870.75>  the equation

B) Solve your equation in Part A to find the price of each floor seat ticket. How do you know your solution is correct?
25*x =  $870.75>  x=870.75/25
X = $34.83
I know that my answer is correct because If you multiply the value of x by 25, you'll get the given total amount that was raised

Part 4) A ride in an amusement park has the following notice at the gate: "Children under the age of 8 are not allowed on this ride." 

Part A: Write an inequality to show the age of children who are allowed on the ride.

let
x> the age of children who are allowed on the ride

we know that
x < 8> are not allowed on the ride
so
x >= 8 > are allowed on the ride

Part B) Describe in words how you can show the solution to this inequality on a number line
x >= 8 
the solution to this inequality are all ages greater than or equal to 8, to be able to show them in a line we would have to shade the numbers from 8 to infinity
the solution is the interval [8, ∞)