6x7=8x9-(6+7+8+9) 7x8=9x10-(7+8+9+10)

Left-hand side:

n(n+1)
=n²+n

Right-hand side:
(n+2)(n+3)-(n+n+1+n+2+n+3)
= n²+5n+6 - (4n+6)
= n²+n

Therefore the relation is an identity (i.e. true for all values of n)

To solve these equations, we need to follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right). Let's break down the steps for each equation.

1. 6x7 = 8x9 - (6+7+8+9)

First, let's calculate the sum inside the parentheses:
6 + 7 + 8 + 9 = 30

Now, substitute this value back into the equation:
6 x 7 = 8 x 9 - 30

Next, calculate the products:
6 x 7 = 42
8 x 9 = 72

Now, substitute these values back into the equation:
42 = 72 - 30

Finally, perform the subtraction:
72 - 30 = 42

So, the equation is true: 6 x 7 = 8 x 9 - (6 + 7 + 8 + 9) simplifies to 42 = 42.

2. 7x8 = 9x10 - (7+8+9+10)

First, let's calculate the sum inside the parentheses:
7 + 8 + 9 + 10 = 34

Now, substitute this value back into the equation:
7 x 8 = 9 x 10 - 34

Next, calculate the products:
7 x 8 = 56
9 x 10 = 90

Now, substitute these values back into the equation:
56 = 90 - 34

Finally, perform the subtraction:
90 - 34 = 56

So, the equation is true: 7 x 8 = 9 x 10 - (7 + 8 + 9 + 10) simplifies to 56 = 56.

Both equations are correct.