Question

15minus a number is less than or equal to 8 times that number what is the number

Answer 1

Let x be the number we are looking for.

Let us go statement by statement so we can find the inequality we want. First we are told "15 minus a number". That would be represented by the expression

`15\text{ -x}`

now, this quantity should be "less than or equal to 8 times that number". So this translates to the expression

`\le8\cdot x`

so if we put together these expressions, we get

`15\text{ -x<=8}\cdot x`

To solve it, we first add x on both sides, so we get

`15\le8x+x`

If we operate on the right, we get

`15\le9x`

Now, we divide both sides by 9, so we get that

`(15)/(9)\le x`

which is equivalent to

`(5)/(3)\le x`

which mean that any number greater than or equal to 5/3 is a solution for this inequality