How to find the value of p such that 4p - 9537 lies between two given values?

Hey there! I'm a supplier of 4p - 9537 products. And today, I wanna talk about how to find the value of p such that 4p - 9537 lies between two given values. This might seem a bit tricky at first, but once you get the hang of it, it's actually pretty straightforward.

Let's say we have two given values, a and b, and we want 4p - 9537 to be greater than a and less than b. In math terms, we can write this as the compound inequality: a < 4p - 9537 < b.

The first step is to break this compound inequality into two separate inequalities. We get a < 4p - 9537 and 4p - 9537 < b.

Let's solve the first inequality, a < 4p - 9537. We wanna isolate p. First, we add 9537 to both sides of the inequality. This gives us a + 9537 < 4p. Then, to get p by itself, we divide both sides by 4. So, we have (a + 9537)/4 < p.

Now, let's solve the second inequality, 4p - 9537 < b. Again, we start by adding 9537 to both sides. We get 4p < b + 9537. Then, we divide both sides by 4, and we have p < (b + 9537)/4.

Combining these two results, we find that the value of p must satisfy the inequality (a + 9537)/4 < p < (b + 9537)/4. This means that p has to be greater than (a + 9537)/4 and less than (b + 9537)/4.

For example, if a = 100 and b = 200, then we first calculate (a + 9537)/4 = (100 + 9537)/4 = 9637/4 = 2409.25 and (b + 9537)/4 = (200 + 9537)/4 = 9737/4 = 2434.25. So, p has to be between 2409.25 and 2434.25.

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References

• Basic Algebra textbooks for compound inequality concepts.