$6 x +3 = 33$.
Work Step by Step
First identify the task. In this case, it is to express "the product of six and a number increased by three is thirty-three" as an equation. We are told to assume the number is "x". A method to solving this problem is to divide the given statement into sub parts and then combine each of these parts into an equation. "The product of four and a number" can be expressed as "$6x$". "increased by five" can be expressed as "$+3$". "Is equal to three" reminds us to connect the two sides with an equals sign, "$=33$". By putting these together, the answer is $6 x +3 = 33$.