Question

Solve each component inequality and graph the solution


`x > 2 and \: x - 1 \leqslant 10`

Answer 1

Solution: The value of x after solving both components is
`2<x\leq11` or
`(2,11]`.

Step-by-step explanation:

From the first component it is clearly noticed that the value of x is greater than 2.

Simplify the second component.

`x-1\leq 10\\x\leq 11`

From the above inequality it is clearly noticed that the value of x is less than or equal to 11.

Solving both components we get
`2<x\leq11` and the graphical representation is shown in the figure.

The red portion shows the solutions of
`x>2`, blue portion shows the solution of
`x-1\leq 10` and purple portion which combination of red and blue portion shows the solution of both inequalities.

Therefore, value of x after solving both components is
`2<x\leq11` or
`(2,11]`.