Final answer:
The expression 7x + 49 is factored by taking out the common factor of 7, resulting in the simpler expression 7(x + 7).
Step-by-step explanation:
The student asked to rewrite the expression 7x + 49 using a common factor. To find the common factor, we look for a number that can divide both terms in the expression. In this case, both 7x and 49 are divisible by 7. So, we factor out the number 7 from each term to rewrite the expression as:
7(x + 7)
This uses the distributive property (a(b + c) = ab + ac), where a is 7, b is x, and c is 7. This simplifies the original expression by factoring out the common number 7 from both terms. Hence, the correct rewritten form is 7(x + 7).
When factoring and simplifying algebraic expressions, it is important to always eliminate terms wherever possible and to check the answer to see if it is reasonable.