(A) Given inequality: $\frac{x+1}{2} > 6(x+2)$ Multiply both sides by $2$: $x+1 > 12(x+2)$ Expand the right side: $x+1 > 12x + 24$ Subtract $x$ from b

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(A) Given inequality: $\frac{x+1}{2} > 6(x+2)$ Multiply both sides by $2$: $x+1 > 12(x+2)$ Expand the right side: $x+1 > 12x + 24$ Subtract $x$ from both sides: $1 > 11x + 24$ Subtract $24$ from both sides: $-23 > 11x$ Divide by $11$: $-\frac{23}{11} > x$ Thus,the solution set is $x \in (-\infty, -\frac{23}{11})$.