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

a) $9 \times n + 6 = 6 + 9n$ Step 1: Simplify both sides of the equation. $9n + 6 = 6 + 9n$ Step 2: Compare both sides. The left side is equal to the right side. This statement is true.

b) $8 \times n + 4 = 4(2n + 1)$ Step 1: Simplify both sides of the equation. $8n + 4 = 4 \times 2n + 4 \times 1$ $8n + 4 = 8n + 4$ Step 2: Compare both sides. The left side is equal to the right side. This statement is true.

c) $6 \times n - 2 = 3(2n - 1)$ Step 1: Simplify both sides of the equation. $6n - 2 = 3 \times 2n - 3 \times 1$ $6n - 2 = 6n - 3$ Step 2: Compare both sides. The left side ($6n - 2$) is not equal to the right side ($6n - 3$). This statement is false.

d) $10 \div 2 + 2 \times 2n = 5 + 4n$ Step 1: Simplify the left side of the equation. $5 + 4n = 5 + 4n$ Step 2: Compare both sides. 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