How do you define a variable and write an expression for each phrase: 6 times a number increased by 3?

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How do you define a variable and write an expression for each phrase: 6 times a number increased by 3?

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Answer 1 · 2016-09-02T08:05:38

Without a comma it is difficult to know what is meant.

$6 times a number,$ $color(red)("6 times a number"),$ increased by 3 $\to 6 x + 3$ $rarrcolor(red)(6x) + 3$

6 times, $a number increased by 3 \to 6 (x + 3)$ $color(blue)"a number increased by 3" rarr color(blue)6(x+3)$

Explanation:

People often ask if punctuation is important. The importance of clearly written phrases cannot be stressed enough!
The use of a comma helps to indicate exactly what is meant.
There is no comma shown, so what is intended is not totally clear.

This expression can be read in two ways:
Note the position of the comma in each case.

Let the number be $x \leftarrow$ $x" " larr"$ always define the variable.

$6 times a number,$ $color(red)("6 times a number"),$ increased by 3"

"Times" means multiply and "increased by 3" means 3 is added.

$6 x + 3$ $color(red)(6x) + 3$

OR

"6 times, $a number increased by 3$ $color(blue)"a number increased by 3"$

$6 (x + 3)$ $6color(blue)((x+3))$

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How do you define a variable and write an expression for each phrase: 6 times a number increased by 3?

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