(A) Given inequality: $3(x-1)+2(x-2)<5(x+2)$ Expand the terms: $3x-3+2x-4<5x+10$ Combine like terms on the left side: $5x-7<5x+10$ Subtrac

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(A) Given inequality: $3(x-1)+2(x-2)<5(x+2)$ Expand the terms: $3x-3+2x-4<5x+10$ Combine like terms on the left side: $5x-7<5x+10$ Subtract $5x$ from both sides: $-7<10$ Since $-7<10$ is a true statement for all real values of $x$,the solution set is the set of all real numbers,$x \in \mathbb{R}$.