Question which-

2.4 Equivalent Expressions - Simplifying polynomials
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Which expression is equivalent to 4 4 x - 5 - 1 x + 1 ?

A.

1 x + 1 4 x - 5

B.

3 3 x - 6

C.

- 1 x + 1 4 x - 5

D.

9 x + 1 4 x - 5

Which expression is equivalent to 4 4 x - 5 - 1 x + 1 ?

Hard-difficulty · SAT Math · Equivalent Expressions — Simplifying polynomials. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice D is correct. The expression 44x-5-1x+1 can be rewritten as 44x-5+-1x+1. To add the two terms of this expression, the terms can be rewritten with a common denominator. Since x+1x+1=1, the expression 44x-5 can be rewritten as x+14x+14x-5. Since 4x-54x-5=1, the expression -1x+1 can be rewritten as 4x-5-14x-5x+1. Therefore, the expression 44x-5+-1x+1 can be rewritten as x+14x+14x-5+4x-5-14x-5x+1, which is equivalent to x+14+4x-5-1x+14x-5. Applying the distributive property to each term of the numerator yields 4x+4+-4x+5x+14x-5, or  4x+-4x+4+5x+14x-5. Adding like terms in the numerator yields 9x+14x-5.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.