Answer: C - Two positive integers are the solutions of the inequality.2x − (x + 1)/4<6 − (x − 1)/2 × 44 × 2x − 4 × (x + 1)/4<4 × 6 − 4 × (x − 1)/28x − 1(x + 1)<24 − 2(x − 1)8x − x − 1<24 − 2x + 27x − 1<26 − 2x7x + 2x<26 + 19x<27x<27/9x<3The positive integers which are the solutions of the inequality are 1 and 2. So, there are 2 solutions.

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How many positive integers are the solutions of (2x − (x + 1)/4) < (6 − (x − 1)/2?)

0
1
2
3
infinitely many

Explanation

Answer: C - Two positive integers are the solutions of the inequality.
2x − (x + 1)/4<6 − (x − 1)/2 × 4
4 × 2x − 4 × (x + 1)/4<4 × 6 − 4 × (x − 1)/2
8x − 1(x + 1)<24 − 2(x − 1)
8x − x − 1<24 − 2x + 2
7x − 1<26 − 2x
7x + 2x<26 + 1
9x<27
x<27/9
x<3

The positive integers which are the solutions of the inequality are 1 and 2. So, there are 2 solutions.

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