Question

Solve.

|y| +15 <28
If all real numbers are solutions, click on "All reals".
If there is no solution, click on "No solution".

Answer 1

`-13 < y < 13`

Explanation:

To solve the absolute value inequality, begin by isolating the absolute value on one side of the equation:

`\begin{aligned}|y| +15 & < 28\\\\|y| +15-15 & < 28-15\\\\|y|& < 13\end{aligned}`

Apply the absolute value rule:

`\boxed{\textsfIf\;\;$}`

Therefore:

`-13 < y < 13`

So, the solution to the given absolute value inequality is:

`\Large\boxed{\boxed{-13 < y < 13}}`

Answer 2

All reals

Explanation:

To solve the absolute value inequality
`\sf |y| + 15 < 28`, we can start by isolating the absolute value term:

`\sf |y| + 15 < 28`

Subtract 15 from both sides:

`\sf |y| + 15 -15 < 28 - 15`

`\sf |y| < 13`

This inequality means that the distance between
`\sf y` and 0 on the number line is less than 13.

Therefore, any real number
`\sf y` that is within the interval
`\sf (-13, 13)` satisfies the inequality.

So, the solution is "All reals."