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Which statement is equivalent to the inequality -10(4x - 2) < 20x - 10?

a) -4x + 2 > 2x - 1
b) -4x + 2 < 2x - 1
c) 4x - 2 > -2x + 1
d) 4x - 2 < -2x + 1

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Final answer:

Upon solving the inequality -10(4x - 2) < 20x - 10, it becomes x > 1/2. Comparing this to the answer choices, the equivalent statement is b) -4x + 2 < 2x - 1.

Step-by-step explanation:

The inequality in question is -10(4x - 2) < 20x - 10. To find an equivalent statement, we must first distribute the -10 within the parentheses:

-10 × 4x = -40x
-10 × (-2) = +20

So our inequality becomes -40x + 20 < 20x - 10. We then move all x terms to one side and constants to the other:

-40x - 20x < -10 - 20
-60x < -30

Dividing both sides by -60, remembering to reverse the inequality (since we're dividing by a negative number), we get:

x > 1/2

To match this with the options given, we rewrite 1/2 as 0.5 and look for equivalent alterations:

a) -4x + 2 > 2x - 1 (Incorrect, doesn't simplify to x > 1/2)
b) -4x + 2 < 2x - 1 (Correct, after simplification)
c) 4x - 2 > -2x + 1 (Incorrect, doesn't simplify to x > 1/2)
d) 4x - 2 < -2x + 1 (Incorrect, doesn't simplify to x > 1/2)

Therefore, the equivalent statement is b) -4x + 2 < 2x - 1.

User Kevin Worth
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