Respuesta :
Given:
The compound inequality [tex]2x-3 < 7[/tex] and [tex]5-x \leq 8[/tex].
To find:
The solution for the given compound inequality
Solution:
We have, compound inequality [tex]2x-3 < 7[/tex] and [tex]5-x \leq 8[/tex].
For [tex]2x-3 < 7[/tex],
Add 3 on both sides.
[tex]2x < 7+3[/tex]
[tex]2x < 10[/tex]
Divide 2 on both sides.
[tex]x< 5[/tex] ...(i)
For [tex]5-x \leq 8[/tex],
Subtract 5 from both sides.
[tex]-x \leq 8-5[/tex]
[tex]-x \leq 3[/tex]
Divide both sides by -1. So, the sign of inequality is changed.
[tex]x \geq -3[/tex] ...(ii)
Using (i) and (ii), we get the solution of given compound inequality as
[tex]x \geq -3[/tex] and [tex]x< 5[/tex]
Therefore, the correct option is D.
