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YOUR ANSWER: 9 < 7 + 4 is a true statement.
You are correct. The statement is read "Nine is less than seven plus four"---that is, 9 is less than 11---which is certainly true.
Most of the difficulty people experience with algebra is due to the fact that they have not learned to read a set of mathematical symbols as a sentence. But, of course, many people feel that it is simply perverse of mathematicians to write in "algebra" instead of "english". The reason for the symbols used in mathematics is that they permit statements to be made compactly and precisely. Even some moderately simple mathematical statements would be hopelessly cumbersome if we attempted to write them in ordinary english prose. Even som quite non-mathematical statements sometimes benefit from borrowing a little of the compact terminology of algebra, as illustrated in the following quotation:
A man made a bargain with another man to give his wife a mink coat in exchange for a used car. But the wife of the man, who really owned the mink coat, objected strongly. So the man who wanted to trade his used car for mink coat for his wife...or rather, the man who wanted to trade his wife for a used car...no...
Let's try it this way:
The party of the first part offered a mink coat in trade for a used card. But the wife of the party of the first part, hereinafter to be referred to as the second party of the first part, objected...
Lawyers seem to like doing things that way. Most of us would prefer this:
X made a bargain with Y to give Mrs. Y a mink coat in exchange for Y's used car. But Mrs. X, who really owned the mink coat, got mad. So Y didn't get a mink coat for Mrs. Y, and X didn't get a used car.
"Well," says our friend Jack (you remember Jack from the Introduction), "all your fine talk about algebra as a language is well and good. But when I took algebra it was full of 'factors' and 'transpositions' anmd people were always nervously snatching 'terms' from one side of an equation to the other, and all kinds of mysterious things like that. What's all that about?"
Well, it's true that there are some techniques involved in algebra and in mathematics generally. Unfortunately, many people were taught the techniques without ever being taught the reasons why the specific techniques were permissible. It happens that the justification or certain elementary techniques will serve very handily to introduce the characteristic feature of algebra, as opposed to arithmetic. This nature is the use of letters or symbols to stand for numbers, and we will take it up in the next chapter.