Answer:
112 – a fraction less than 12
Step-by-step explanation:
We need to look for only one value that will invalidate the claim.
We denote the unknown in the condition with [tex]x[/tex].
Let's consider each individually:
1. 89 × a number less than 1
[tex]89\times x\le 1[/tex]
[tex]x\le \dfrac{1}{89}[/tex]
We only need values that satisfy this inequality to invalidate the claim. Like 0, -1,...
2. 112 - a fraction less than 12
[tex]112-x\le1[/tex]
[tex]112-1\le x[/tex]
[tex]111\le x[/tex]
[tex]x\ge111[/tex]
But this is a contradiction because [tex]x[/tex] must be less than 12.
Hence, this is always true.
3. 25 + a fraction less than 12
[tex]25+x\le1[/tex]
[tex]x\le1-25[/tex]
[tex]x\le-24[/tex]
Hence, all fractions less than or equal to [tex]-24[/tex] will invalidate the claim. Like -24, -25,...
4. 10 × a number less than 1
[tex]10\times x\le 1[/tex]
[tex]x \le\dfrac{1}{10}[/tex]
We only need values that satisfy this inequality to invalidate the claim. Like 0, -1,...
