SAT Math

Category - Algebra and Functions

How many positive integers are the solutions of (2x − (x + 1)/4) andlt; (6 − (x − 1)/2?)
  1. 0
  2. 1
  3. 2
  4. 3
  5. infinitely many
Explanation
Answer: C - Two positive integers are the solutions of the inequality.
2x − (x + 1)/4andlt;6 − (x − 1)/2 × 4
4 × 2x − 4 × (x + 1)/4andlt;4 × 6 − 4 × (x − 1)/2
8x − 1(x + 1)andlt;24 − 2(x − 1)
8x − x − 1andlt;24 − 2x + 2
7x − 1andlt;26 − 2x
7x + 2xandlt;26 + 1
9xandlt;27
xandlt;27/9
xandlt;3

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