Question

Find all real numbers X such that 4x+2>14 AND -21x+1>22

Answer 1

To solve the system of inequalities, we find the values of x that satisfy both conditions: x > 3 and x < -1.

Step-by-step explanation:

To solve this problem, we need to find the values of x that satisfy the given inequalities:

4x+2 > 14

-21x+1 > 22

For the first inequality, subtracting 2 from both sides gives us:

4x > 12

Dividing both sides by 4, we get:

x > 3

For the second inequality, subtracting 1 from both sides gives us:

-21x > 21

Dividing both sides by -21 (and flipping the inequality sign), we get:

x < -1

Therefore, the values of x that satisfy both inequalities are:

x > 3 and x < -1

Answer 2

What you must do for this case is to solve both inequalities
We have then:
4x + 2> 14
We clear x:
4x + 2> 14
x> (14-2) / 4
x> 3

-21x + 1> 22
We clear x:
-21x> 22-1
x <-21/21
x <-1
Therefore we have to
For 4x + 2> 14
x belongs (3, inf)
For -21x + 1> 22
x belongs (-inf, -1)
The solution that is met for both inequalities is:
x belongs (-inf, -1) U (3, inf)