Answer:
[tex] A)\displaystyle2 < x < 3[/tex]
Step-by-step explanation:
A compound inequality is an inequality that combines two simple inequalities
we are given that
[tex] \displaystyle 4x - 4 < 8 \ \: \text{and} \: \: 9x + 5 > 23[/tex]
solving x for the first equation:
[tex] \displaystyle 4x - 4 < 8[/tex]
add 4 to both sides:
[tex] \displaystyle 4x < 12[/tex]
divide both sides by 4 and since we are dividing both sides by a positive number the inequality won't swap
[tex] \displaystyle x < 3[/tex]
solving x for the second equation:
[tex] \displaystyle 9x + 5 > 23[/tex]
cancel 5 from both sides:
[tex] \displaystyle 9x > 18[/tex]
divide both sides by 9 and since we are dividing both sides by a positive number:
[tex] \displaystyle x > 2[/tex]
therefore by combining the equations we obtain:
[tex] \displaystyle\boxed{2 < x < 3}[/tex]
hence,
our answer is A)
