Question

name
showing all your work, solve each inequality and then place it on the calendar in the corresponding date.
$99\div n\div 9 = 20$
$\frac{1}{3}n \geq 5$
$\frac{1}{2}n \geq 15$
$-3 \times n \leq -12$
$n \times -1 \leq -1$
$\frac{5}{8}n \geq 22\frac{1}{2}$
$100 - 3n \leq 25$
$102 + n \leq 131$
$121 \div s \leq 11$
$n - 2 \leq 8$
$\frac{1}{2}n \leq 10.5$
$8n \leq 56$
$\frac{1}{4}n \leq 7$
$n - 1 \geq 1$
$510 \div n \geq 30$
$90n \leq 720$
$\frac{1}{13}n \leq 2$
$\frac{n}{3} \leq 6$
$5n \leq 60$
$\frac{1}{4}n \leq 6$
$3n \leq 42$
$525 \div n \leq 105$
$5n \leq 115$
$48 \div n \geq 16$
$\frac{1}{3}n \leq 9$
$n + 2 \leq 8$
$4n \leq 52$
$28 \div n \leq 8$
$10n \geq 190$
$n - 3 \leq 19$

Explanation:

Step1: Solve \( \frac{1}{3}n \geq 5 \)

Multiply both sides by 3: \( n \geq 5\times3 \)
\( n \geq 15 \)

Step2: Solve \( \frac{1}{2}n \geq 15 \)

Multiply both sides by 2: \( n \geq 15\times2 \)
\( n \geq 30 \)

Step3: Solve \( -3n \leq -12 \)

Divide both sides by -3 (reverse inequality): \( n \geq \frac{-12}{-3} \)
\( n \geq 4 \)

Step4: Solve \( -n \leq -1 \)

Multiply both sides by -1 (reverse inequality): \( n \geq 1 \)

Step5: Solve \( \frac{5}{8}n \geq 22\frac{1}{2} \) (convert \( 22\frac{1}{2} \) to \( \frac{45}{2} \))

Multiply both sides by \( \frac{8}{5} \): \( n \geq \frac{45}{2}\times\frac{8}{5} \)
\( n \geq 36 \)

Step6: Solve \( 100 - 3n \leq 25 \)

Subtract 100: \( -3n \leq 25 - 100 \)
\( -3n \leq -75 \)
Divide by -3 (reverse inequality): \( n \geq 25 \)

Step7: Solve \( 102 + n \leq 131 \)

Subtract 102: \( n \leq 131 - 102 \)
\( n \leq 29 \)

Step8: Solve \( 121 \div n \leq 11 \) (rewrite as \( \frac{121}{n} \leq 11 \), assume \( n > 0 \))

Multiply both sides by \( n \): \( 121 \leq 11n \)
Divide by 11: \( n \geq 11 \)

Step9: Solve \( N - 2 \leq 8 \)

Add 2: \( N \leq 8 + 2 \)
\( N \leq 10 \)

Step10: Solve \( \frac{1}{2}n \leq 10.5 \)

Multiply by 2: \( n \leq 10.5\times2 \)
\( n \leq 21 \)

Step11: Solve \( 8n \leq 56 \)

Divide by 8: \( n \leq 7 \)

Step12: Solve \( \frac{1}{4}n \leq 7 \)

Multiply by 4: \( n \leq 28 \)

Step13: Solve \( n - 1 \geq 1 \)

Add 1: \( n \geq 2 \)

Step14: Solve \( 510 \div n \geq 30 \) (rewrite as \( \frac{510}{n} \geq 30 \), \( n > 0 \))

Multiply by \( n \): \( 510 \geq 30n \)
Divide by 30: \( n \leq 17 \)

Step15: Solve \( 90n \leq 720 \)

Divide by 90: \( n \leq 8 \)

Step16: Solve \( \frac{1}{13}n \leq 2 \)

Multiply by 13: \( n \leq 26 \)

Step17: Solve \( \frac{n}{3} \leq 6 \)

Multiply by 3: \( n \leq 18 \)

Step18: Solve \( 5n \leq 60 \)

Divide by 5: \( n \leq 12 \)

Step19: Solve \( \frac{1}{4}n \leq 6 \)

Multiply by 4: \( n \leq 24 \)

Step20: Solve \( 3n \leq 42 \)

Divide by 3: \( n \leq 14 \)

Step21: Solve \( 525 \div n \leq 105 \) (rewrite as \( \frac{525}{n} \leq 105 \), \( n > 0 \))

Multiply by \( n \): \( 525 \leq 105n \)
Divide by 105: \( n \geq 5 \)

Step22: Solve \( 5n \leq 115 \)

Divide by 5: \( n \leq 23 \)

Step23: Solve \( 48 \div n \geq 16 \) (rewrite as \( \frac{48}{n} \geq 16 \), \( n > 0 \))

Multiply by \( n \): \( 48 \geq 16n \)
Divide by 16: \( n \leq 3 \)

Step24: Solve \( \frac{1}{3}n \leq 9 \)

Multiply by 3: \( n \leq 27 \)

Step25: Solve \( n + 2 \leq 8 \)

Subtract 2: \( n \leq 6 \)

Step26: Solve \( 4n \leq 52 \)

Divide by 4: \( n \leq 13 \)

Step27: Solve \( 28 \div n \leq 8 \) (rewrite as \( \frac{28}{n} \leq 8 \), \( n > 0 \))

Multiply by \( n \): \( 28 \leq 8n \)
Divide by 8: \( n \geq 3.5 \)

Step28: Solve \( 10n \geq 190 \)

Divide by 10: \( n \geq 19 \)

Step29: Solve \( n - 3 \leq 19 \)

Add 3: \( n \leq 22 \)

Answer:

Solutions for each inequality (selected examples):
\( \frac{1}{3}n \geq 5 \): \( n \geq 15 \)
\( \frac{1}{2}n \geq 15 \): \( n \geq 30 \)
\( -3n \leq -12 \): \( n \geq 4 \)
(And so on for all inequalities as solved above)