Question

Which values of k are solutions to the inequality |-k-2|<18? Check all that apply
-40

Answer 1

The solution to the inequality |-k-2|<18 is any value of k within the range of -20 to 16. From the options provided, -20 is the only value that satisfies the inequality.

Step-by-step explanation:

The absolute value inequality |-k-2|<18 can be solved by considering two separate cases: when the expression inside the absolute value is non-negative and when it is negative. So we split the inequality into two inequalities:

• k + 2 < 18
• -(k + 2) < 18

Solving these we get:

• k < 16
• k > -20

Therefore, the solution set for the inequality is -20 < k < 16. This tells us that any value of k within this range satisfies the original inequality. Looking at the given options, the only value that fits this range is -20.

Answer 2

any number except -20

Step-by-step explanation:

`|-k-2|<18`

`-k-2<18`
`-k-2>18`

`-k<18+2`
`-k>18+2`

`-k<20`
`-k>20`

Multiply by -1 to make the k positive. This will alter all the terms which means 20 will become negative. NOTE: When multiplying or dividing by negative numbers, the inequaliy sign flips.

`k>-20`
`k<-20`

k must be either greater than -20 but not including it or fewer than -20 but not including it; therefore, any number between negative infinity and -21 and -19 and postive infinity