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Which uses the GCF to generate an expression equivalent to 10/7 x- 5/7 ?

A. 5/7 (2x-1)
B. 5/7 (2x+1)
C. 1/7 (10x-1)
D. 1/7 (10x+1)

1 Answer

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Final answer:

The expression equivalent to 10/7 x - 5/7 using the GCF is A. 5/7 (2x-1), where 5 is the GCF of the numerical coefficients 10 and 5.Option A is the correct answer.

Step-by-step explanation:

The question is asking to use the Greatest Common Factor (GCF) to create an expression equivalent to 10/7 x - 5/7. To find the GCF, we look at the numerical coefficients of the terms in the expression.

Both 10 and 5 are divisible by 5, making 5 the GCF. Thus, we factor out 5/7 from both terms:

5/7 (2x) - 5/7 (1)

Simplifying, we get:

5/7 (2x - 1)

Therefore, the expression that uses the GCF to generate an equivalent expression is A. 5/7 (2x-1).

To simplify the expression (10/7)x - 5/7 using the Greatest Common Factor (GCF), we identify the GCF of the numerical coefficients, which is 5. Factoring out 5/7 from both terms, we get (5/7)(2x - 1). Therefore, option A (5/7)(2x-1) correctly represents the expression using the GCF.

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