Question

The sum of three times a number and 4 is between -8 and 10

Answer 1

Alright, so we can start by writing it out by their signs.
Using PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction) and noting that the inequality comes last, we can write it as the sum of (addition), then three times (multiplication) a number and 4 (ties in with the sum of, making it also addition).Note that we know that "a number and 4" means addition because it doesn't state to do anything with it, and we don't know what "the sum of" referred to with numbers, so they match up. Therefore, we have multiplication (3 times a number=3 * number), then addition (3 times a number, or 3 * number, added to 4, or 3*number+4), and we can do the inequality. Between -8 and 10 means that it is greater than -8 and less than 10, as 10 is the larger number, writing it out as -8< (less than) 3*number+4 < (3*number+4 is less than 10, so we have another less than sign) 10. Subtracting 4 from everything using the subtraction property of equality, we get -12<3*number<6. Next, we can divide everything by 3 to separate the number and get -4<number<2.

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