Answer:
7x -(12¾)
Explanation:
You want the algebraic expression for "12¾ less than the product of 7 and a number x".
Translation
The product of 7 and x is represented as ...
7x
If you want 12¾ less than that, then you subtract 12¾.
7x -12¾ . . . . . . . the desired expression
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Additional comment
A "product" is what we call the result of multiplication. The operation of multiplication can be indicated several ways. If there is no ambiguity, the most common way to show multiplication is to write the values next to each other without any symbol.
7x . . . . 7 times x
Sometimes, it is helpful to put the values in parentheses:
(7)(x)
A multiplication symbol can be used, if desired.
7·x
(7)×(x)
When showing multiplication using the symbol ×, care must be taken to differentiate it from the symbol x, especially if confusing these symbols will give a different result than desired. (Sometimes, when the symbol × is unavailable, an 'x' is used instead.)
Occasionally, you will see a dot on the baseline used as a multiplication symbol. Likewise, you may see a centered dot intended as a decimal point.
7.x . . . . . 7 times x
7·3x . . . . 7 and 3 tenths times x (maybe)
When different numbers are involved, the use of a baseline dot for multiplication, and a centered dot for a decimal point can be confusing.
7.3.x . . . . could be (7)(3)(x) or (7.3)(x)
7·3.x . . . . could be (7)(3)(x) or (7.3)(x)
In general, a notation should be chosen so as to reduce any ambiguity to a minimum and communicate in a way that the audience understands.
When a mixed number is involved, as above, it can be useful to enclose it in parentheses, so it is not confused with the product of an integer and a fraction. The font used to express the fraction can be chosen to help reduce the ambiguity.