To solve the inequality ∣−4x+10∣≤9|-4x + 10| \leq 9∣−4x+10∣≤9, we need to consider two cases:
−4x+10≤9 -4x + 10 \leq 9 −4x+10≤9 Subtract 10 from both sides: −4x≤−1 -4x \leq -1 −4x≤−1 Divide by -4 (and reverse the inequality sign): x≥14 x \geq \frac{1}{4} x≥41
4x−10≤9 4x - 10 \leq 9 4x−10≤9 Add 10 to both sides: 4x≤19 4x \leq 19 4x≤19 Divide by 4: x≤194 x \leq \frac{19}{4} x≤419
Combining both cases, the solution set is: 14≤x≤194 \frac{1}{4} \leq x \leq \frac{19}{4} 41≤x≤419
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