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Chapter 11: Problem 38

Solve using the addition principle. $$ -\frac{1}{8}+y=-\frac{3}{4} $$

Short Answer

Expert verified
y = -\frac{5}{8}

Step by step solution

01

- Isolate the Variable

The goal is to get the variable, which is y, by itself on one side of the equation. To do this, add \(\frac{1}{8}\) to both sides to cancel out \(-\frac{1}{8}\) on the left side.\(-\frac{1}{8} + y + \frac{1}{8} = -\frac{3}{4} + \frac{1}{8}\)
02

- Simplify the Right Side

Combine the fractions on the right-hand side. Find a common denominator for \(-\frac{3}{4}\) and \(\frac{1}{8}\). The common denominator is 8.\(-\frac{3}{4} = -\frac{6}{8}\). Thus: \(-\frac{6}{8} + \frac{1}{8} = -\frac{5}{8}\)
03

- Write the Simplified Equation

Now the equation simplifies to: \(y = -\frac{5}{8}\).

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Key Concepts

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

Solving Equations
When you face an algebraic equation, the main goal is to find the value of the variable that makes the equation true. In simpler terms, you鈥檙e trying to balance both sides of the equation. Think of it like a scale where you need both sides to weigh the same. By performing the same operation on both sides of the equation, you maintain that balance. For example, in \(-\frac{1}{8} + y = -\frac{3}{4}\), if you add \(\frac{1}{8}\) to both sides, you keep the equation balanced. Thus, solving equations often involves a series of steps where you ensure any operation performed on the equation is applied equally to both sides.
Isolating Variables
Isolating the variable means getting the variable by itself on one side of the equation. This is often the key step in solving algebra problems. If the variable is not isolated, it is difficult to determine its exact value. For instance, in the equation \(-\frac{1}{8} + y = -\frac{3}{4}\), our goal is to have \(y\) by itself on one side. To do that, we need to remove the fraction next to \(y\). By adding \(\frac{1}{8}\) to both sides, you cancel out \(-\frac{1}{8}\) on the left side, which isolates \(y\). The equation then becomes \(y = -\frac{3}{4} + \frac{1}{8}\).
Fractions and Common Denominators
Fractions can complicate algebra problems, but finding a common denominator can simplify things. A common denominator makes it easier to add or subtract fractions. In the equation \(-\frac{1}{8} + y + \frac{1}{8} = -\frac{3}{4} + \frac{1}{8} \, you needed a common denominator to combine \(-\frac{3}{4}\) and \(\frac{1}{8}\). The least common multiple of 4 and 8 is 8. So, \(-\frac{3}{4} \) can be converted to \(-\frac{6}{8} \) because \(-3 \times 2 = -6 \) and \4 \times 2 = 8\). This allows you to combine the fractions easily: \(-\frac{6}{8} + \frac{1}{8} = -\frac{5}{8} \). Now, the simplified equation is \ ( y=-\frac{5}{8}) \.

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Most popular questions from this chapter

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