These expressions represent the number of middle school students who signed up for 4 different spring intramural sports.

8n-10 - baseball
2n+3 - flag football
n+4 - kickball
3(2n-1) - soccer

the number of students signed up for baseball and kickball is equal to the number of students signed up for flag football and soccer.

part a: model the situation with an equation by writing the correct expression in place of each question mark.

? + ? = ? + ?

part b: solve the equation. then identify the number of students signed up for each sport.

n = ?
baseball: ?
flag football: ?
kickball: ?
soccer: ?

part a :

8n-10 + n+4 = 2n+3 + 3(2n-1)

part b :

n = 6

baseball = 38

flag football = 15

kickball = 10

soccer = 33

Step-by-step explanation:

part a :

8n-10 + n+4 = 2n+3 + 3(2n-1)

part b :

9n - 6 = 2n+3 + 6n-3

9n - 6 = 8n

n = 6

now plug in to every equation to solve for how many student play in that sport

baseball : 8(6)-10 = 38

flag football : 2(6)+3 = 15

kickball : (6)+4 = 10

soccer : 3[2(6)-1]=33

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form