how to resolve this

Question

3(x-4)>15
28<4(5-2x)
3(2n+1)>4n+9
3n-10<7(2+n)

Answer 1

1).

3(x - 4) > 15

Divide each side by 3.

[3(x - 4)] / 3 > 15/3

Cancel common terms.

(x - 4) > 5

Add 4 to each side.

(x - 4 + 4) > 5 + 4

cancel terms

x > 9.

Solution set is {x | x : x > 9}.

2).

28 < 4(5 - 2x)

Apply distributive property : a(b - c)  =ab - ac.

28 < (20 - 8x)

(20 - 8x) > 28

Subtract 20 from each side.

- 8x > 28 - 20

- 8x > 8

Divide each side by negative 8,flips the symbol.

x < - 1.

Solution set is {x | x : x < - 1}.

3).

3(2n + 1) > 4n + 9

Apply distributive property : a(b + c)  =ab - ac.

6n + 3 > 4n + 9

Subtract 4n from each side.

6n - 4n + 3 > 4n + 9 - 4n

2n + 3 > 9

Subtract 3 from each side.

2n > 9 - 3

2n > 6

Divide each side by 2.

n > 6/2

n > 3.

Solution set is {n | n : n > 3}.

4).

3n - 10 < 7(2 + n)

Apply distributive property : a(b + c)  =ab + ac.

3n - 10 < 14 + 7n

Subtract 3n from each side.

3n - 10 - 3n < 14 + 7n - 3n

- 10 < 14 + 4n

Subtract 14 from each side.

- 10 - 14 < 14 + 4n - 14

- 24 < 4n

Divide each side by 4.

- 24/4 < 4n/4

- 6 < n

Solution set is {n | n : n > - 6}.