Question

1. $25 - 3(n - 2) geq -8n + 6$
2. $7k + 1 leq 8$ or $-7 < k - 10$
3. $9 < -3m < 24$
4. $|2x + 5| < 13$
5. $-2|3m| + 3 < -51$

Explanation:

Step1: Expand left-hand side

$25 - 3n + 6 \geq -8n + 6$

Step2: Simplify left-hand side

$31 - 3n \geq -8n + 6$

Step3: Add $8n$ to both sides

$31 + 5n \geq 6$

Step4: Subtract 31 from both sides

$5n \geq -25$

Step5: Divide by 5

$n \geq -5$

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Step1: Solve first inequality

$7k + 1 \leq 8$
$7k \leq 7$
$k \leq 1$

Step2: Solve second inequality

$-7 < k - 10$
$k > 3$

Step3: Combine solutions

$k \leq 1$ or $k > 3$

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Step1: Divide all parts by -3 (reverse signs)

$\frac{9}{-3} > m > \frac{24}{-3}$

Step2: Simplify values

$-3 > m > -8$ or $-8 < m < -3$

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Step1: Rewrite absolute value inequality

$-13 < 2x + 5 < 13$

Step2: Subtract 5 from all parts

$-18 < 2x < 8$

Step3: Divide by 2

$-9 < x < 4$

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Step1: Subtract 3 from both sides

$-2|3m| < -54$

Step2: Divide by -2 (reverse sign)

$|3m| > 27$

Step3: Rewrite absolute value inequality

$3m > 27$ or $3m < -27$

Step4: Solve for m

$m > 9$ or $m < -9$

Answer:

1. $\boldsymbol{n \geq -5}$
2. $\boldsymbol{k \leq 1}$ or $\boldsymbol{k > 3}$
3. $\boldsymbol{-8 < m < -3}$
4. $\boldsymbol{-9 < x < 4}$
5. $\boldsymbol{m > 9}$ or $\boldsymbol{m < -9}$