Question

William is thinking of a number, n and he wants his sister to guess the number. His first clue is that five less than two times his number is at least negative three and at most fifteen. Write and solve a compound inequality that shows the range of numbers that William might be thinking of.

Answer 1

[1,10] is interval notation

Step-by-step explanation:

Answer 2

`1 \le n \le 10`

Step-by-step explanation:

Given

Guess: n

Required

Write a compound inequality for the number

The first clue:

Multiply n by 2: 2n

Subtract 5: 2n - 5

The result is at least -3:
`2n - 5 \ge -3` (at least means
`\ge`)

And

The result is at most -3:
`2n - 5 \le 15` (at most means
`\le`)

So, we have:

`2n - 5 \ge -3` and
`2n - 5 \le 15`

Solve for n

`2n - 5 \ge -3`

`2n \ge -3 + 5`

`2n \ge 2\\`

`n \ge 1`

`2n - 5 \le 15`

`2n \le 15 + 5`

`2n \le 20`

`n \le 10`

So, we have:

`n \ge 1` and
`n \le 10`

Rewrite as:

`1 \le n` and
`n \le 10`

Combine

`1 \le n \le 10`