Answer:
1. x > 4
2. m < 2
3. x > 2
4. x < -6
Step-by-step explanation:
These 4 inequalities will be solved the same way we solve equations. We take variables to one side and numbers to another and use algebra to solve. Each of them are solved shown below:
1.
so x is greater than 4, we can write (variable first):
x > 4
2.
so m is less than 2, we can write:
m < 2
3.
so x is greater than 2, we can write:
x > 2
4.
so x is less than -6, we can write:
x < -6
Answer:
(1, -2), (4, 1)
Step-by-step explanation:
Here we want to solve the system of equations:
y = x^2 - 4*x + 1
y = x - 3
First, we can see that in both parts we have isolated the variable "y", so we can just write:
x - 3 = y = x^2 - 4*x + 1 = y
removing the "y"s, we get:
x - 3 = x^2 - 4*x + 1
Now we can solve this for x
0 = x^2 - 4*x + 1 - x + 3
0 = x^2 - 5*x + 4
This is a quadratic equation, the solutions are given by the Bhaskara's formula, that says that for a general quadratic equation:
0 = a*x^2 + b*x + c
The solutions are given by:
So for the case of our equation:
0 =x^2 - 5*x + 4
The solutions are given by:
So the two solutions are:
x₁ = (5 + 3)/2 = 4
x₂ = (5 - 3)/2 = 1
To find the ordered pair, we need to replace these values in one of the equations of the system, let's use the second:
y = x₁ - 3 = 4 - 3 = 1
Then we have one solution at (4, 1)
And for the other:
y = x₂ - 3 = 1 - 3 = -2
then the ordered pair is (1, -2)
Now we want to write from least to greatest with respect to the x-coordinate, then the correct order is:
(1, -2), (4, 1)