The sum of 1/3 of a number and 12

Start by assigning a variable name to the "number" -- call it x.

Now write out what they say:

"The product of 1/3 and the sum of a number and 3" -- that's 1/3 times x + 3, or (1/3)(x + 3) or (x + 3) / 3

It's "between negative one and five"

So that means:

-1 < (x + 3) / 3 < 5

So now solve this inequality.  First multiply everything by 3.

-3 < x + 3 < 15

Subtract 3 from all the terms:

-6 < x < 12

So the answer is, all numbers between -6 and 12

Step-by-step explanation:

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step-by-step explanation: