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-5 <= (3n-2)/(4) <= 4

−5≤3n−24≤4 -5 \leq \frac{3 n-2}{4} \leq 4

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Full solution

Q. −5≤3n−24≤4 -5 \leq \frac{3 n-2}{4} \leq 4
  1. Eliminate Fraction: First, we need to eliminate the fraction by multiplying all parts of the inequality by 44, which is the denominator of the fraction.\newline−5×4≤3n−24×4≤4×4-5 \times 4 \leq \frac{3n-2}{4} \times 4 \leq 4 \times 4
  2. Simplify Inequality: After multiplying, we simplify the inequality. −20≤3n−2≤16-20 \leq 3n - 2 \leq 16
  3. Add 22: Next, we add 22 to all parts of the inequality to isolate the term with the variable nn.\newline−20+2≤3n−2+2≤16+2-20 + 2 \leq 3n - 2 + 2 \leq 16 + 2
  4. Isolate Variable Term: Simplify the inequality after adding 22. −18≤3n≤18-18 \leq 3n \leq 18
  5. Divide by 33: Now, we divide all parts of the inequality by 33 to solve for nn.−183≤3n3≤183-\frac{18}{3} \leq \frac{3n}{3} \leq \frac{18}{3}
  6. Final Simplification: Finally, we simplify the inequality after dividing by 33.\newline−6≤n≤6-6 \leq n \leq 6

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