Question

How do you translate word phrases to algebraic expressions: the quotient of a number and 7 added to twice the number is greater than or equal to 30?

Answer 1

The statement is a bit ambiguous:

`x/7 +2x >=30" or "x/(7+2x) >=30`

Explanation:

This is a good example of how the absence of any punctuation leads to an ambiguous statement:

Call 'the number' `x`

Look at the key words:

"quotient" is the answer to a division: look for the word 'and'

"twice the number" means multiply by 2, so `2 xx x = 2x`

"greater than or equal" indicates an inequality: `>=`

`color(blue)("The quotient of a number and 7,")color(red)(" added to twice the number,")color(limegreen)(" is greater than or equal to 30")`
`color(blue)(x div 7)color(red)(+2x)color(limegreen)(>= 30)= x/7 +2x >=30`

The sentence above is different from

`color(blue)("The quotient of a number and,")color(red)(" 7 added to twice the number,")color(limegreen)(" is greater than or equal to 30")`
`color(blue)(x div)color(red)((7+2x))color(limegreen)(>= 30) = x/(7+2x) >=30`

It really is about making the intention as clear as possible.
In the absence of any punctuation, I would opt for the first.