Question

Find all real numbers X such that 4x+2≥14 and -21x+1<22

Answer 1

`\begin{cases}4x+2\ge14\\-21x+1<22\end{cases}`

In the first inequality, we have

`4x+2\ge14\implies4x\ge12\implies x\ge3`

In the second, we have

`-21x+1<22\implies-21x<21\implies x>-1`

The solution to the system is the intersection of these two intervals, which would be
`x\ge3`.