# Solve the inequality.

1.

–6w < 84

w > 14

w < –14

w > –14

w < 14

## – 6 w < 84

Divide both sides by - 6

When you mutiply or divide both sides by a negative number the sign changes directions.

w > 84 / - 6

w > - 14

## –6w < 84

## To solve for w, we need to isolate w on one side of the inequality symbol. Since -6 is negative, we need to divide both sides by -6, but remember that dividing by a negative number will flip the inequality symbol.

-6w < 84

w > -14 (dividing by -6 and flipping the symbol)

Therefore, the solution is w > -14.

## 5m>45

## To solve for m, we need to isolate m on one side of the inequality symbol. We can do that by dividing both sides by 5.

5m > 45

m > 9 (dividing both sides by 5)

Therefore, the solution is m > 9.

## n/-3 ≥ 4

k/6>4

Carlos needs to buy at least 7 pairs of socks. They come in packages of 3. What is the fewest number of packages he should get?

## 1. n/-3 ≥ 4

To solve for n, we need to isolate n on one side of the inequality symbol. We can do that by multiplying both sides by -3 and flipping the inequality symbol since -3 is negative.

n/-3 ≥ 4

n ≤ -12 (multiplying both sides by -3 and flipping the symbol)

Therefore, the solution is n ≤ -12.

2. k/6 > 4

To solve for k, we need to isolate k on one side of the inequality symbol. We can do that by multiplying both sides by 6.

k/6 > 4

k > 24 (multiplying both sides by 6)

Therefore, the solution is k > 24.

3. Carlos needs to buy at least 7 pairs of socks. They come in packages of 3. What is the fewest number of packages he should get?

Since each package contains 3 socks and Carlos needs at least 7 pairs (14 socks), he will need to get at least 5 packages of socks. This will give him a total of 15 socks, which is enough to make 7 pairs with one sock left over. Therefore, the fewest number of packages Carlos should get is 5.