Final answer:
To solve the inequality, isolate x on one side of the equation by performing algebraic operations step-by-step. The solution is x > 12.
Step-by-step explanation:
To solve the inequality, we need to isolate x on one side of the equation. Let's do that step-by-step.
Multiplying both sides of the inequality by 6 (the denominator of the first fraction) gives us: x + 3 > 6(x/4) + 6
Simplifying, we get: x + 3 > 3/2(x) + 6
Subtracting 3/2(x) and 6 from both sides: x - 3/2(x) - 6 > 0
Combining like terms: 1/2(x) - 6 > 0
Multiplying both sides by 2 to eliminate the denominator: x - 12 > 0
Adding 12 to both sides: x > 12
So, x is greater than 12.