Question

Eight less than four times a number is less than 56. What are the possible values of that number?

Answer 1

Let \(n\) be the unknown number, which I'm assuming to be natural \((n \in \mathbb{N})\). We therefore know that:
\(8 < 4n < 56.\)
This double inequality is actually the conjunction of two simple inequalities:
\(8 < 4n \quad \textrm{and}\quad 4n < 56.\)
Can you proceed from now?

Answer 2

\(\color{#0cbb34}{\text{Originally Posted by}}\) @nicolegunter
Any number less than 16 will work.
\(\color{#0cbb34}{\text{End of Quote}}\)
I don't think so. For instance \(4 \times 1 = 4\), which is not greater than \(8\) and \(15 \times 4 = 60\), which is not less than \(56\).

Answer 3

@DuarteME

Answer 4

\(\color{#0cbb34}{\text{Originally Posted by}}\) @RichardWatterson7
It would start off like 4x-8<56 (then you add 8 on both sides then it'll end up like 4x<64 (then you divide 4 on both sides) then you'll get x<16
\(\color{#0cbb34}{\text{End of Quote}}\)
I see what you mean! However, I think that the question is regarding \(8 < 4x < 56\) rather than \(4x - 8 <56\).

Answer 5

ANY NUMBER LESS THE 16 WILL WORK

Answer 6

\(\color{#0cbb34}{\text{Originally Posted by}}\) @RichardWatterson7
2<x<14
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I agree with you! :)

Answer 7

👌 Gn 2 all nd talk 2 y'all 2morrow