Question

Solve for x. 4x-4< 8 AND 9x +5 > 23 is it a, b,c or d ?

Answer 1

Answer:

$A)\displaystyle2 < x < 3$

Step-by-step explanation:

A compound inequality is an inequality that combines two simple inequalities

we are given that

$\displaystyle 4x - 4 < 8 \ \: \text{and} \: \: 9x + 5 > 23$

solving x for the first equation:

$\displaystyle 4x - 4 < 8$

add 4 to both sides:

$\displaystyle 4x < 12$

divide both sides by 4 and since we are dividing both sides by a positive number the inequality won't swap

$\displaystyle x < 3$

solving x for the second equation:

$\displaystyle 9x + 5 > 23$

cancel 5 from both sides:

$\displaystyle 9x > 18$

divide both sides by 9 and since we are dividing both sides by a positive number:

$\displaystyle x > 2$

therefore by combining the equations we obtain:

$\displaystyle\boxed{2 < x < 3}$

hence,

our answer is A)