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Chapter 2: Problem 51

Solve using the addition principle. $$ t-\frac{1}{8}>\frac{1}{2} $$

Short Answer

Expert verified
t > \(\frac{5}{8}\)

Step by step solution

01

- Identify the goal

The objective is to isolate the variable, in this case, being 't' on one side of the inequality.
02

- Add \(\frac{1}{8}\) to both sides

To eliminate the negative fraction next to 't', add \(\frac{1}{8}\) to both sides of the inequality: \(t - \frac{1}{8} + \frac{1}{8} > \frac{1}{2} + \frac{1}{8}\)
03

- Simplify the inequality

Combine the fractions on the right-hand side: \(t > \frac{1}{2} + \frac{1}{8}\). To add these fractions, convert \(\frac{1}{2}\) to \(\frac{4}{8}\): \(\frac{4}{8} + \frac{1}{8} = \frac{5}{8}\). Thus the inequality becomes \(t > \frac{5}{8}\).
04

Conclusion

The variable 't' has been isolated and the inequality is solved. The solution is \(t > \frac{5}{8}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

addition principle

In simple terms: Whatever you do to one side, make sure you do the same to the other side! This technique helps keep the inequality balanced.
isolate the variable

Isolating the variable is a crucial step because it allows you to clearly see the value or range of values that the variable can take.
combining fractions

Combining fractions correctly is essential because it ensures that you do not change the original value by accident. Always convert to a common denominator first, then add or subtract the numerators.

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Most popular questions from this chapter

A storekeeper goes to the bank to get \(\$ 10\) worth of change. She requests twice as many quarters as half dollars, twice as many dimes as quarters, three times as many nickels as dimes, and no pennies or dollars. How many of each coin did the storekeeper get?

Use an inequality and the five-step process to solve each problem. The women's volleyball team can spend at most \(\$ 450\) for its awards banquet at a local restaurant. If the restaurant charges a \(\$ 40\) setup fee plus \(\$ 16\) per person, at most how many can attend?

Translate to an inequality. The time of the test was between 45 min and 55 min.

One number is \(25 \%\) of another. The larger number is 12 more than the smaller. What are the numbers?

Use an inequality and the five-step process to solve each problem. Band members at Colchester Middle School are expected to average at least 20 min of practice time per day. One week Monroe practiced \(15 \mathrm{min}, 28 \mathrm{min}, 30 \mathrm{min}, 0 \mathrm{min}, 15 \mathrm{min},\) and \(25 \mathrm{min}\). How long must he practice on the seventh day if he is to meet expectations?
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