Final answer:
To solve the inequality system, the first inequality 3x - 4 < 8 simplifies to x < 4, and the second inequality 2x + 2 > 4 simplifies to x > 1. The common solution for the system is the range of values where x is greater than 1 and less than 4, expressed as 1 < x < 4.
Step-by-step explanation:
To solve the inequality system, we have two inequalities to solve separately. The first inequality is 3x - 4 < 8 and the second is 2x + 2 > 4. Let's solve each step by step.
Solving the first inequality
Add 4 to both sides of the inequality 3x - 4 < 8:
3x - 4 + 4 < 8 + 4
3x < 12
Now, divide both sides by 3 to isolate x:
3x / 3 < 12 / 3
x < 4
Solving the second inequality
Subtract 2 from both sides of the inequality 2x + 2 > 4:
2x + 2 - 2 > 4 - 2
2x > 2
Then, divide both sides by 2 to isolate x:
2x / 2 > 2 / 2
x > 1
To find the solution to the system, we need the range of x that satisfies both inequalities, which is 1 < x < 4. This means that x must be greater than 1 and less than 4.