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Chapter 8: Problem 271

In the following exercises, solve the equation. $$ y+8-15=-3 $$

Short Answer

Expert verified
y = 4

Step by step solution

01

Simplify the Equation

Combine like terms on the left side. In this case, combine 8 and -15 to get: \[ y + 8 - 15 = y - 7 \]. So the equation transitions to: \[ y - 7 = -3 \].
02

Isolate the Variable

To solve for y, add 7 to both sides of the equation to isolate y. This gives: \[ y - 7 + 7 = -3 + 7 \], which simplifies to: \[ y = 4 \].

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Key Concepts

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

Combining Like Terms
When solving linear equations, combining like terms is an essential first step. Like terms are terms that have the same variable raised to the same power. In the given exercise, we start with the equation:
y + 8 - 15 = -3.
Here, 8 and -15 are constants and can be combined. This combination simplifies the equation:
y + 8 - 15 = y - 7.
Combining these terms reduces the clutter, making the equation easier to handle.
Isolating Variables
Isolating the variable is a crucial step for finding its value. After combining like terms, we're left with:
y - 7 = -3. The goal is to solve for y, so we need to get y by itself on one side of the equation.
To do this, add 7 to both sides of the equation. Adding the same number to both sides keeps the equation balanced, resulting in:
y - 7 + 7 = -3 + 7, which simplifies to: y = 4.
Now y is isolated, and we know that y equals 4.
Simplifying Equations
In solving linear equations, simplifying them at every step is key to reaching the solution more efficiently. Let's recap our simplified progression:
1. Starting equation: y + 8 - 15 = -3.
2. Combine like terms: y - 7 = -3.
3. Isolate the variable: y = 4.
Simplification helps in breaking down the problem into smaller, manageable steps. Always perform operations that make the equation look cleaner and simpler as you progress toward the final answer.

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Most popular questions from this chapter

In the following exercises, solve each equation using the Division Property of Equality. $$ -y=4 $$

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