greathound157885 greathound157885
  • 19-09-2022
  • Mathematics
contestada

Solve for x: 1 < x + 3 < 4

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

Respuesta :

semsee45
semsee45 semsee45
  • 20-09-2022

Answer:

-2 < x < 1

Step-by-step explanation:

Given inequality:

[tex]1 < x+3 < 4[/tex]

[tex]\textsf{If $a < u < b$ \;then\; $a < u$ \;and \;$u < b$}:[/tex]

Case 1

[tex]\implies 1 < x+3[/tex]

[tex]\implies 1-3 < x+3-3[/tex]

[tex]\implies -2 < x[/tex]

[tex]\implies x > -2[/tex]

Case 2

[tex]\implies x+3 < 4[/tex]

[tex]\implies x+3-3 < 4-3[/tex]

[tex]\implies x < 1[/tex]

Combine the intervals:

[tex]-2 < x < 1[/tex]

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