8. \( -x+4>3 \) and \( -2 x+3 \leq 9 \)

To solve the first inequality \( -x + 4 > 3 \), we can start by isolating \( x \). Subtracting 4 from both sides gives us \( -x > -1 \). Multiplying both sides by -1 (and remembering to flip the inequality sign) results in \( x < 1 \). Now, for the second inequality \( -2x + 3 \leq 9 \), we again isolate \( x \). First, we can subtract 3 from both sides to get \( -2x \leq 6 \). Dividing by -2 (and flipping the inequality sign) gives us \( x \geq -3 \). Combining these results, we have \( -3 \leq x < 1 \). Thus, the solution set includes all \( x \) values within that range. In interval notation, the solution is expressed as \( [-3, 1) \).