Find the value of the variable that makes these number sentences true: a) h+8=19 b) 2p−6=4 c) 1/3y = 12

The left side is equal to the right side.
This statement is true.

b) $8 \times n + 4 = 4(2n + 1)$

$$8n + 4 = 4 \times 2n + 4 \times 1$$ $$8n + 4 = 8n + 4$$

The left side is equal to the right side.
This statement is true.

c) $6 \times n - 2 = 3(2n - 1)$

$$6n - 2 = 3 \times 2n - 3 \times 1$$ $$6n - 2 = 6n - 3$$

The left side ($6n - 2$) is not equal to the right side ($6n - 3$).
This statement is false.

d) $10 \div 2 + 2 \times 2n = 5 + 4n$

The left side is equal to the right side.
This statement is true.

Here are the answers:

a) True

b) True

c) False

d) True