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

Question 1:

A) It works in the first inequality because the symbol is "greater than or equal to". This is also why it does not work in the second inequality. Using 3 for x gives us a value of exactly 11; for an inequality that says greater than or equal to, this is allowed. For a strictly less than inequality, it is not.

B) 7

Question 2:

A) 25x = 870.75

B) x = 34.83

Question 3:

A) x ≥ 8

B) Circle 8 on the number line and fill it in; then shade the number line to the left.

Explanation

Question 1:

A) the explanation is in the answer.

B) 8x+1=57

Subtract 1 from each side:

8x+1-1=57-1

8x = 56

Divide both sides by 8:

8x/8 = 56/8

x=7

Question 2:

A) Letting x be the cost, we would multiply the cost by the number of tickets, 25, for a total of 870.75.

B) 25x = 870.75

Divide both sides by 25:

25x/25 = 870.75/25

x = 34.83

Question 3:

A) Since no child less than 8 is allowed, any student 8 or older would be allowed. This means the inequality would be x≥8

B) The explanation is in the answer.