Solve the following equation, show inverse operations to prove your answer:
3x – 31 = 4(x + 3)
3x - 31 = 4(x + 3)
3x - 31 = 4x + 12 (distribute on the right side)
3x - 4x = 12 + 31 (move x term to one side and numbers to the other side)
-x = 43
x = -43 (divide by -1 to solve for x)
Inverse operations:
3x - 31 = 4(x + 3)
3x - 31 = 4x + 12
-31 = x + 12 (subtract 4x from both sides)
-43 = x (subtract 12 from both sides)
Find the range of the function f(x) =3x + 2 for the domain {–1, 0, 1, 2, 3}. Show substitution work to prove your answer.
To find the range of the function f(x) = 3x + 2 for the given domain {–1, 0, 1, 2, 3}, we substitute each value from the domain into the function and then determine the resulting values:
1. For x = -1:
f(-1) = 3(-1) + 2 = -3 + 2 = -1
2. For x = 0:
f(0) = 3(0) + 2 = 0 + 2 = 2
3. For x = 1:
f(1) = 3(1) + 2 = 3 + 2 = 5
4. For x = 2:
f(2) = 3(2) + 2 = 6 + 2 = 8
5. For x = 3:
f(3) = 3(3) + 2 = 9 + 2 = 11
Now, we list the resulting values:
f(-1) = -1
f(0) = 2
f(1) = 5
f(2) = 8
f(3) = 11
The range of the function f(x) = 3x + 2 for the given domain {–1, 0, 1, 2, 3} is { -1, 2, 5, 8, 11 }.