what is the algebraic equation for three times the sum of a number and seven is two less than five times the number.

Let n represent the number.

"the sum of a number and 7" is (n+7)

Three times "the sum of a number and 7" is 3 (n+7)

"is" translates to "=".

"five times the number" is 5n

Two less than "five times the number" is 5n-2

Your equation is

3 (n+7) = 5n-2