Final answer:
The correct equation representing a number 'm' increased by 23 being equal to 15 more than twice the number 'm' is 'm + 23 = 2m + 15' which corresponds to option C.
Step-by-step explanation:
The question involves establishing an equation to represent a given situation, specifically to find the value of a number, 'm,' when it is increased. It says that a number 'm' increased by 23 is equal to 15 more than twice the number 'm.' This can be translated into an equation.
To start, we will express 'a number m increased by 23' as m + 23. The phrase '15 more than twice the number m' means we take 'm,' double it, and then add 15, giving us 2m + 15. The word 'is' signifies an equality, so we set the two expressions equal to each other resulting in the equation m + 23 = 2m + 15.
From the provided options, this matches with option C, which confirms that this is the correct equation that represents the given situation:
Correct Answer
m + 23 = 2m + 15
When you come across problems of this nature, remember the importance of converting words into mathematical expressions accurately, and respect the commutative property A + B = B + A, which ensures that the order of addition does not change the sum. However, be attentive not to misapply this property when constructing equations that involve operations other than addition, such as multiplication or exponents, as the commutative property does not hold in these more complex operations.