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Solve the compound inequality: 1/4 < 2x - 7/2 < 5

User Jurell
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1 Answer

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Let's start solving the given problem step by step:
1. We have the compound inequality 1/4 < 2x - 7/2 < 5.

2. The goal is to isolate x in the middle of the inequality. Firstly, let's make 2x the subject of the inequality. We can do this by adding 7/2 to all parts of the inequality. We get 1/4 + 7/2 < 2x < 5 + 7/2.

3. Simplify the fractions on both sides: 15/4 < 2x < 17/2

4. The next step is to get x alone. We can achieve this by dividing all parts of the inequality by 2: 15/8 < x < 17/4

Therefore, the solution to the compound inequality 1/4 < 2x - 7/2 < 5 is 15/8 < x < 17/4. This means x can be any number between 15/8 and 17/4.

User Muyustan
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