How would you solve these compound inequalities word problems?

1. The human ear can distinguish sounds between 20Hz and 20,000 Hz, inclusive.
2. For a man to box as a welterweight, he must weigh more than 140 lbs, but at most 147 lbs.

The solution would simply be the statement of the inequality

e.g. 2.

if x is the number of lbs, then

140 < x ≤ 147

notice 140 is excluded , but 147 is included

Do #1 the same way

To solve compound inequalities word problems, it's essential to understand the given information and the conditions imposed by the problem. Then, you can break down the compound inequalities into individual inequalities and solve each one separately.

Let's tackle each problem:

1. The human ear can distinguish sounds between 20Hz and 20,000 Hz, inclusive.

To solve this problem, we need to find all the values of frequency (Hz) that fall within the given range.

The range is inclusive, meaning the values at the endpoints (20 and 20,000 Hz) are included.

So, the inequality can be expressed in two parts:
20 ≤ frequency ≤ 20,000

This can also be written as two individual inequalities:
20 ≤ frequency and frequency ≤ 20,000

For the first inequality, 20 ≤ frequency, since we are looking for all frequencies greater than or equal to 20, the solution is straightforward. The frequency is any number greater than or equal to 20.

For the second inequality, frequency ≤ 20,000, the solution is also straightforward. The frequency is any number less than or equal to 20,000.

Hence, combining the solutions, we can say that the human ear can distinguish sounds with frequencies greater than or equal to 20Hz and less than or equal to 20,000Hz.

2. For a man to box as a welterweight, he must weigh more than 140 lbs but at most 147 lbs.

To solve this compound inequality, we need to find the weight range that satisfies the given conditions.

The compound inequality is:
140 < weight ≤ 147

We can rewrite it as two individual inequalities:
140 < weight and weight ≤ 147

For the first inequality, 140 < weight, we are looking for all weights greater than 140. Therefore, the solution is any weight greater than 140 lbs.

For the second inequality, weight ≤ 147, the solution is straightforward. The weight is any number less than or equal to 147 lbs.

Combining the solutions, we can say that for a man to box as a welterweight, he must weigh more than 140 lbs but at most 147 lbs.

So, the key to solving compound inequalities is breaking them down into individual inequalities and finding the overlapping range that satisfies both conditions.