Question

three times the difference of number and thirteen is the same as twenty eight' as an algebraic expression ​

Answer 1

The algebraic expression representing 'three times the difference of number and thirteen is the same as twenty eight' is written as 3(x - 13) = 28. It's an algebraic equation that adheres to the universal rules of mathematics.

Step-by-step explanation:

The student's question 'three times the difference of number and thirteen is the same as twenty eight' can be translated into an algebraic expression. To construct this expression, we take the following steps:

1. Identify the unknown number as a variable, commonly 'x'.
2. The phrase 'the difference of number and thirteen' means we subtract 13 from our variable, which gives us 'x - 13'.
3. When we see 'three times,' we multiply the entire difference by 3, thus giving us '3(x - 13)'.
4. 'Is the same as' indicates equality, so we set the expression equal to the given number, which in this case is 28.

The complete algebraic equation that represents this situation is:

3(x - 13) = 28

This equation follows the universal rules of mathematics, which as we know are the same regardless of time or place, as long as the correct rules are applied. The same rule (e.g., A + B = B + A) ensures that we can have confidence in the equality. Subsequently, this equation can be solved to find the value of 'x' that makes the statement true.