I don't see why it wouldn't be algebra. We traditionally use our own Latin (aka "regular") letters or Greek letters for variables, but there's no reason we have to do it this way. In fact, in grade school saw exactly this line of reasoning, when you'd solve equations like 3 + (square) = 7, and you'd know to fill in the square with the number 4.
It depends on your definition. When algebra was first invented, there was no notation (letters or symbols for variables, etc.); it was all done in words. So technically algebra is not the use of notation, but of particular techniques for manipulating equations (e.g. adding the same quantity to each side).
Even so, the technique you presumably use to solve this is algebra, so I'd still say yes. I think. On the other hand, for this one you really don't need anything more than arithmetic.
Algebra is not the use of letters to stand for numbers; for centuries that was not part of algebra at all. Algebra (or rather the subject of elementary algebra, which is what is taught in high school and "college algebra") is the study of how to work with numbers that are not yet known.
The available historical evidence indicates that the study of algebra was invented about 600 CE in India. For centuries, algebra was done using words in natural languages such as "thing." Thus, there is no logical necessity to use artificial symbols at all. Can you find the number or numbers that make the following statement true: "one plus the product of an unknown number and two equals 35"? Of course you can.
The use of letters as concise and convenient symbols for unknown numbers was developed in Europe during the late 16th and early 17th century. So the problem posed in the previous paragraph becomes "what is x if 2x + 1 = 35." It is a much clearer and more concise notation than using words from a natural language. But there is no logical necessity to use letters as symbols. They are simply very easy symbols to write because they were developed for the exact purpose of making writing easy. The use of letters as symbols representing unknown or as yet unspecified numbers has permitted an explosion in mathematical knowledge and is an essential tool in understanding and using modern mathematics, but it is a psychological advantage rather than a logical necessity.
Beginning students, however, do not find using letters to represent numbers a pschological advantage because it contradicts everything that they have previously learned, where numerals represented numbers and letters represented sounds. It is a major difficulty in learning the modern way of doing algebra. To make an analogy: babies become very mobile while crawling and then revert to slow, stumbling locomotion when transitioning to walking. Because the use of letters to represent unknown or unspecified numbers is the major difficulty that students must initially overcome in learning algebra, they tend (mistakenly) to think that it is the essence of the subject.