Question

Solve for x: 1 < x + 3 < 4

4 > x > 7
4 < x < 7
−2 > x > 1
−2 < x < 1

Answer 1

-2 < x < 1

Explanation:

Given inequality:

`1 < x+3 < 4`

`\textsf{If $a < u < b$ \;then\; $a < u$ \;and \;$u < b$}:`

Case 1

`\implies 1 < x+3`

`\implies 1-3 < x+3-3`

`\implies -2 < x`

`\implies x > -2`

Case 2

`\implies x+3 < 4`

`\implies x+3-3 < 4-3`

`\implies x < 1`

Combine the intervals:

`-2 < x < 1`