Equations in
One Variable
One Variable
Inequalities in
One Variable
One Variable
Equations in
Two Variables
Two Variables
Functions
Sequences
100
Solve for the following equation:
7-8x=1-5x
x=2
100
Solve for the following inequality:
2x+20>=14
x>=-3
100
Consider the function y=2x+8 . Determine if the ordered pair (3, 16) is a solution.
y=2x+8
16=2(3)+8
16=6+8
16!=14
(3,16) is NOT a solution
100
Determine whether the following set {(0, -1), (1, 1), (3, 5)} is a function. Explain your reasoning.
Yes, the following set is a function because every input value has exactly one output value.
100
Write the first four terms of the sequence. f(n)=2(n+3)
f(1)=2(1+3)=8
f(2)=2(2+3)=10
f(3)=2(3+3)=12
f(4)=2(4+3)=14
200
Solve for the following equation:
55-6(3b-1)=-11
b=4
200
Solve for the following inequality:
3x>=7x-20
x<=5
200
Determine if the ordered pair (2,5) is a solution to the equation 2x-3y=-11 .
2(2)-3(5)=-11
4-15=-11
-11=-11
(2,5) is a solution.
200
Determine whether the following set represents a function:
{(1,5), (2,4), (3,5), (3,4), (4,4), (5,5)}
The set is not a function because (3,5) and (3,4) both have the same input of 3.
The input value of 3 is repeating, therefore it is not a function.
200
f(1)=3(1)+2=5
f(2)=3(2)+2=8
f(3)=3(3)+2=11
f(4)=3(4)+2=14
300
Solve for the following equation:
2r-6+5r=3-r+7
r=2
300
Solve for the following inequality:
3x-(x+7)>x-14
x > -7
300
Complete the table for the following equation:
y=4-2x
300
Determine whether the following mapping diagram represents a function.
Yes the mapping diagram is a function. Every input goes directly to one output.
300
Write the value of the 5th term in the sequence f(n)=(n-1)^2 .
f(5)=(5-1)^2
f(5)=(4)^2
f(5)=16
400
Solve for the following equation:
7t-13-2t=9+5t
-13!=9
No Solution
400
Solve for the following inequality:
9y+4>=-3(1-3y)
4>=-3
True; All real numbers are solutions.
Many solutions
400
Determine if the ordered pair (12,16) is a solution for the following equation: x- y/2 = 4 .
Yes, (12,16) is a solution.
12-16/2 = 4
12-8=4
4=4
true, 4=4.
400
The function f(x) and g(x) are defined by explicit rules f(x)=7x-2 and g(x)=3x+6 . Find the value of x for which f(x)=g(x) .
x=2
400
Find the 15th term of the sequence defined by the explicit rule f(n)=2n^2+1 .
f(15)=2(15)^2+1
f(15)=2(225)+1
f(15)=450+1
f(15)=451
500
Solve for the following equation:
4(2x-3)-3x=-2x-12+7x
-12=-12
Infinitely Many Solutions
500
Solve for the following inequality:
3(x-4)>5(x+2)-2x
-12>10
False; there are no solutions to make the inequality true.
500
Which of the following has infinitely many solutions:
13x+2=10x-7
2(x+5)-13=-3+2x
4x+5=-9+4x
2(x+5)-13=-3+2x
2x+10-13=-3+2x
10-13=-3
-3=-3
Since -3=-3 is true, then there is infinitely many solutions.
500
The function f(x) and g(x) are defined by explicit rules f(x)=5x+1 and g(x)=49-3x . Find the value of x for which f(x)=g(x) .
x=6
500
Find the first 3 terms of the sequence f(1)=2 and f(n)=f(n-1)+6 .
f(1)=2
f(2)=f(2-1)+6=f(1)+6=2+6=8
f(3)=f(3-1)+6=f(2)+6=8+6=14