Question

How do you solve `|- 7k | + 2< 37`?

Answer 1

`-5 < k < 5`

Explanation:

`abs(-7k)+2<37`

`abs(-7k)+2<37color(white)(aaaa)`Isolate the absolute value term by subtracting`color(white)(aaaaaaaaaaaaaaaa)` 2 from both sides
`color(white)(aaaaa)-2color(white)(a)-2`

`abs(-7k)<35`

Absolute value inequalities are solved with two equations.
For the second equation, change the sign of the right side and flip the direction of the inequality symbol.

`-7k<35` and `-7k > -35`

`(-7k)/-7 < 35/-7` and `(-7k)/-7 > (-35)/-7`

When dividing by a negative, flip the direction of the inequality.

`k> -5color(white)(aaaaa)` `k<5`

These two inequalities can also be written as:

`-5 < k < 5`