Question

Question #161f8

Answer 1

`x<15`

Explanation:

`(-2)*(x-6)=12`

`-2x+12>-18`

`-2x>-30`

`x<15`

Answer 2

`x > -3 " "or " "x > -6`

It depends how you interpret the statement.

Explanation:

This is a good example of how a sentence can be ambiguous because there is no comma to indicate what is grouped together.

Compare the following, taking note of the use of commas:

`color(blue)("The product of -2 and a number, minus six, is greater than -18"`

and

`color(red)("The product of -2, and a number minus six is greater than -18")`

The expression you write will depend on how you interpret the information: Use `x` as the number.

`color(blue)("The product of -2 and a number, minus six, is greater than -18"`
will lead to

`color(blue)(-2 xx x -6 > -18" "rarr 2x -6 > -18)`

`color(red)("The product of -2, and a number minus six is greater than -18")`
will lead to

`color(red)(2 xx(x-6) > - 18" "rarr 2(x-6) > -18)`

My choice would be the first option. The second could be improved by being given as:

6 less than the product of -2 and a number is greater than -18.

The value of the number will differ.

`color(blue)(2x -6 > -18)`
`color(blue)(2x > -18 +6)`
`color(blue)(2x > -12)`
`color(blue)(x > -6)`

`color(red)(2(x-6) > -18)`
`color(red)(2x-12 > -18)`
`color(red)(2x > -18+12)`
`color(red)(2x > -6)`
`color(red)(x > -3)`