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…

Question

asked Nov 19, 2022 144k views

2 Answers

Tomglynch · Answer 1 · 2022-11-25T22:47:11+0000

Answer:

$1 \le n \le 10$

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

$1 \le n \le 10$