Number in front of a variable
Coefficient
A student has less than 20 pencils in their backpack
Let x = the number of pencils
x < 20
2(x+3)
2x+6
2x+3=11
Find x
x=4
2x+1>7
x>3
A letter representing a number
Variable
A movie ticket costs $8 each, and a student can spend no more than $40
Let x = number of tickets
x<=5
3(x+4)
3x-4=11
Find x
x=5
3x-5<=10
x<=5
A number alone (No variable)
Constant
Each notebook costs $3, and a student has at least $15 to spend.
Let x = number of notebooks
x>=5
5(x+2)
5x+10
2x+5=x+9
x=4
2x+4 > x+9
x>5
A number that gets "flipped"
Reciprocal
A teacher is making groups of 4 students, and there are at most 28 students
Let x = number of groups
x<=7
2(x+3)+4
2x+10
4(x+2)=20
x=3
3(x+1)<=12
x<=3
What mathematical property is represented here

Distributive Property
To participate in the annual sports day, Mr. Adams would like to have nine students in each group. But fewer than 54 students are in class today, so Mr. Adams is unable to make as many full groups as he wants. How many full groups can Mr. Adams make? Write the inequality that describes the situation.
Let x = number of groups
x<6
3(2x+5)-3
6x+12
3(x+2)-4=2x+5
x=3
2(x+3)-4 > x+6
x>4